AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

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AP State Syllabus 10th Class Maths Bits 7th Lesson Coordinate Geometry with Answers

Question 1.
Write the nearest point to origin,
i) (2, – 3)
ii) (5, 0)
iii) (0, – 5)
iv) (1, 3)
Answer:
(1,3)

Question 2.
The distance of a point (3, 4) from the origin is how many units ?
Answer:
5 units.

Question 3.
Write the formula to find the area of a triangle.
Answer:
Δ = \(\frac { 1 }{ 2 }\) bh and
Δ = \(\sqrt{s(s-a)(s-b)(s-c)}\)

Question 4.
Find the mid point of (2, 3) and (-2,3).
Answer:
(0, 3)

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 5.
Find the distance to X – axis from the point (3, – 4).
Answer:
4 units

Question 6.
Find the centroid of the triangle formed by these points (0, 3); (3, 0) and (0, 0).
Answer:
(1, 1)

Question 7.
Where do the points lie on co-ordinate axis ?
(- 4, 0), (2, 0), (6, 0), (- 8, 0)
Answer:
On X-axis.

Question 8.
The graph of y = 5 represents.
Answer:
Parallel to X – axis.

Question 9.
Find sum of the distances from A(3, 4) to X – axis and from B(5, 7) to Y – axis.
Answer:
9 units.

Question 10.
Find the distance from origin to (2,3).
Answer:
\(\sqrt{13}\) units.

Question 11.
Find slope of the line passing through the points (0, sin 60°) and (cos 30°, 0).
Answer:
m = – 1

Question 12.
If the mid point of (x – y, 8) and (2, x + y) is (5, 10), then find (x, y).
Answer:
(10,2)

Question 13.
Where the point (0, 5) lies ?
Answer:
On Y – axis.

Question 14.
Find the area of a triangle whose verti-ces (points) Eire (0, 0), (3, 0) and (0, 4).
Answer:
6 sq. units.

Question 15.
Write the slope of Y – axis.
Answer:
Not defined.

Question 16.
Find the mid point of line segment joined by (4, 5) and (- 6, 3).
Answer:
(-1,4)

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 17.
(x, y), (2,0), (3,2) and (1,2) are vertices of a parallelogram, then find (x, y).
Answer:
(0, 0)

Question 18.
Find centroid of a triangle, whose ver-tices are (- a, 0), (0, b) and (a, 0).
Answer:
(0, \(\frac { b }{ 3 }\))

Question 19.
Find the distance between two points A (a cos 0, 0), B (0, a sin 0).
Answer:
a units.

Question 20.
Find the distance between (0, 0), (x1, y1) points.
Answer:
\(\sqrt{\mathrm{x}_{1}^{2}+\mathrm{y}_{1}^{2}}\)

Question 21.
If A(log2 8, log5 25) and B(log10 10, log10 100), then find the mid-point of AB.
Answer:
(2,2)

Question 22.
Find the distance between (0, 7) and (- 7, 0).
Answer:
7\(\sqrt{2}\) units.

Question 23.
Find slope of the line passing through the points (- 1, 1) and (1, 1).
Answer:
0

Question 24.
Find the slope of the line passing through the points (4, 6) and (2, – 5).
Answer:
\(\frac { 11 }{ 2 }\)

Question 25.
In the given figure, find the area of ΔOAB.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 1
Answer:
6 sq. units.

Question 26.
A line makes 45° with X – axis, then find its slope.
Answer:
m = tan θ = tan 45° = 1

Question 27.
If a line is passing through (2, 3) and (2, – 3), then write the nature of that line.
Answer:
The line is parallel to Y – axis and The slope of the line is not defined.

Question 28.
Find area of the triangle formed by the points A(0, 0), B(1, 0) and C(0, 1).
Answer:
\(\frac { 1 }{ 2 }\) sq. units.

Question 29.
Find the distance from X – axis to (- 4, 3) is units.
Answer:
3 units.

Question 30.
Find the area of the triangle BOA is …………… sq. units.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 2
Answer:
3 sq. units.

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 31.
Find the slope of the line that passes through the points P (x1, y1) and Q(x2, y2) and making an angle ‘θ’ with X – axis.
Answer:
m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Question 32.
The area of given triangle is 60 sq. units, then find x = …………units.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 3
Answer:
12 units.

Question 33.
A line makes 45° with X – axis, then find its slope.
Answer:
1

Question 34.
Find the distance between the points (x1, y1) and (x2, y2) which are on the line parallel to Y – axis.
Answer:
|y – y2| or |y2 – y1 |

Question 35.
If the co-ordinates of the vertices of a rectangle are (0, 0), (4, 0), (4, 3) and (0, 3), then find the length of its di¬agonal.
Answer:
5 units.

Question 36.
Find the distance from Y-axis to (4, 0) is ……………. units.
Answer:
4 units.

Question 37.
Draw the graph represented by y = x.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 4

Question 38.
If origin is the centroid of a triangle, whose vertices are (3, 2), (- 6, y) and (3, – 2), then calculate ‘y’.
Answer:
y = 0

Question 39.
In a coordinate plane, if line segment AB is parallel to X – axis, then write about points A and B.
Answer:
X – coordinates of points A and B are equal.

Question 40.
Find the distance between the points (0, 7) and (- 7, 0).
Answer:
7\(\sqrt{2}\) units.

Question 41.
Find the distance of the point (- 8, 3) from the origin.
Answer:
\(\sqrt{73}\) units

Question 42.
If points (x, 0), (0, y) and (1, 1) are collinear, then find \(\frac{1}{x}+\frac{1}{y}\).
Answer:
1

Question 43.
Write a point on the X – axis is of the form.
Answer:
(x, 0)

Question 44.
Find the points (- 3, 0), (0, 5) and (3, 0) are the vertices of which type of triangle ?
Answer:
Isosceles triangle.

Question 45.
Find the area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b).
Answer:
0

Question 46.
Write a point on the Y – axis is of the form.
Answer:
(0, y)

Question 47.
The point which divides the line segment joining the points (3, 4) and (7, – 6) internally in the ratio 1 : 2 lies in the quadrant.
Answer:
Q4

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 48.
Find the distance between the points (- 2, 3) and (2, – 3).
Answer:
\(\sqrt{52}\) units.

Question 49.
AOBC is a rectangle whose three ver-tices are A(4, 0), B(0, 3) and O (0, 0), then find its diagonal ?
Answer:
5 units.

Question 50.
Find the distance of the point (-8, -7) from Y – axis.
Answer:
8 units.

Question 51.
A circle is drawn with origin as centre and passing through (2, 3), then find its radius.
Answer:
\(\sqrt{13}\) units.

Question 52.
Find the perimeter of a triangle whose vertices are A(12, 0), 0(0,.0) and B(0, 5).
Answer:
30 units.

Question 53.
Find the distance of the point (- 4, 3) from X – axis.
Answer:
3 units.

Question 54.
If the distance between the points (4, y) and (1, 0) is 5, then find ‘y’.
Answer:
y = ± 4.

Question 55.
Write the distance of (x, y) from X-axis.
Answer:
y units.

Question 56.
Find the distance of the point (- 9, 40) from the origin.
Answer:
41 units

Question 57.
If (0, 0), (a, 0) and (0, b) are collinear, then write the relation between ‘a’ and b’.
Answer:
ab = 0

Question 58.
Which ratio the centroid divides each median ?
Answer:
2:1

Question 59.
Find the value of ‘p’ if the distance be-tween (2, 3) and (p, 3) is 5. ,
Answer:
p = 7

Question 60.
Find the angle between X – axis and Y – axis.
Answer:
90°

Question 61. Find the distance between the points (a cos θ, 0) and (0, a sin θ).
Answer:
‘a’ units

Question 62.
(- 2, 8) belongs to which quadrant ?
Answer:
Q2

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 63.
Find the centroid of the triangle whose vertices are (2, – 3), (4, 6), (- 2, 8).
Answer:
(\(\frac{4}{3}, \frac{11}{3}\))

Question 64.
Guess shape of the closed figure formed by the points (- 2, 0), (2, 0), (2, 2), (0, 4) and (-2,-2).
Answer:
Pentagon

Question 65.
Find the midpoint of the line joining of (2, 3) and (- 2, 3).
Answer:
(0, 0)

Question 66.
If the centroid of the triangle formed with (a, b); (b, c) and (c, a) is O (0, 0), then the value of a3 + b3 + c3.
Answer:
3 abc

Question 67.
If the points (a, 2a), (3a, 3a) and (3,1) are collinear, then find k.
Answer:
k = \(\frac { -1 }{ 3 }\)

Question 68.
Write the coordinates of the midpoint joining P(x1, y1) and Q(x2, y2).
Answer:
\(\left(\frac{\mathrm{x}_{1}+\mathrm{x}_{2}}{2}, \frac{\mathrm{y}_{1}+\mathrm{y}_{2}}{2}\right)\)

Question 69.
Find the slope of line joining of (5, -1), (0, 8).
Answer:
\(-\frac{9}{5}\) =m

Question 70.
If the distance between the points (3, k) and (4, 1) is \(\sqrt{10}\), then find the value of k.
Answer:
4 (or)-2.

Question 71.
If (- 2, – 1), (a, 0), (4, b) and (1,2) are the vertices of a parallelogram, then find a’.
Answer:
a = 1

Question 72.
Write the slope of X – axis.
Answer:
0

Question 73.
P(2, 2), Q(- 4, 4) and R(5, – 8) are the vertices of a ΔPQR, then find length of median from ‘R’.
Answer:
\(\sqrt{157}\) units.

Question 74.
Find the value of ‘k’ if the distance be-tween (2, 8) and (2, k) is 3.
Answer:
k = 5.

Question 75.
Find the distance of a point (α, β) from the origin.
Answer:
\(\sqrt{\alpha^{2}+\beta^{2}}\)

Question 76.
If the points (1, 2), (-1, x) and (2, 3) are collinear, then find the value of x.
Answer:
x = 0.

Question 77.
If (- 2,8) and (6, – 4) are the end points of the diameter of a circle, then find the centre of the circle.
Answer:
(2, 2) = centre.

Question 78.
A(0, -1), B(2, 1) and C(0, 3) are the vertices of AABC, then find median
through ‘B’ has a length . units.
Answer:
2

Question 79.
Two vertices of a triangle are (3, 5) and (- 4, – 5). If the centroid of the triangle is (4, 3), find the third vertex.
Answer:
(13, 9).

Question 80.
If A, B, C are collinear, then find the area of AABC.
Answer:
Δ = 0

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 81.
A circle drawn with origin as centre 13
passes through (\(\frac { 13 }{ 2 }\),0). Find the point which doesn’t lie in the interior of the circle.
Answer:
(-6,3)

Question 82.
Find area of triangle formed by (-4, 0), (0, 0) and (0, 5) is ……………… sq. units.
Answer:
10 sq.units.

Question 83.
Find the ratio in which the point (4, 8) divide the line segment joining the points (8, 6) and (0, 10).
Answer:
1:1

Question 84.
Write a formula to the coordinates of the point which divides the line join¬ing (x1, y1) and (x2, y2) in the ratio m: n internally.
Answer:
P = \(\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)\)

Question 82.
If A(4, 0), B(8, 0), then find \(\overline{\mathbf{A B}}\).
Answer:
4 units.

Question 83.
Find the slope of the line \(\frac{\mathbf{x}}{\mathbf{a}}+\frac{\mathbf{y}}{\mathbf{b}}\) = 1.
Answer:
m = \(\frac{-\mathrm{b}}{\mathrm{a}}\)

Question 87.
Find .the radius of the circle whose centre is (3, 2) and passes through (- 5, 6) is……………..units.
Answer:
4\(\sqrt{5}\) units.

Question 88.
In Heron’s formula ‘s’ represents.
Answer:
s = \(\frac{a+b+c}{2}\) = Semi perimeter

Question 89.
Slope of the line joining the points (2, 5) and (k, 3) is 2, then find k.
Answer:
k = 1.

Question 90.
If A(4, 5), B(7, 6), then find \(\overline{\mathbf{A B}}\).
Answer:
\(\sqrt{10}=\overline{\mathrm{AB}}\)

Question 91.
Write the distance of (x, y) from Y-axis.
Answer:
‘x’units.

Question 92.
A(2, 0), B(l, 2), C(l, 6), then find ∆ABC.
Answer:
∆ = 0, so the points are collinear.

Question 93.
Find the mid point of the line joining the points (1,1) and (0, 0).
Answer:
( \(\frac{1}{2}, \frac{1}{2}\) )

Question 94.
How much the slope of vertical line ?
Answer:
Not defined.

Question 95.
A(1, – 1), B(0, 6) and C(- 3, 0), then find G (centroid).
Answer:
G = (\(\frac{-2}{3}, \frac{5}{3}\))

Question 96.
A(a, b) and B(- a, – b), then find \(\overline{\mathbf{B A}}\).
Answer:
\(\overline{\mathrm{BA}}=2 \sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}\)

Question 97.
Find the centroid of the triangle formed with the line x + y = 6 with the coordinate axes.
Answer:
G .= (2, 2)

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 98.
Find the area of triangle formed with (- 5,-1), (3,-5) and (5, 2).
Answer:
32 sq. units.

Question 99.
How much the slope of horizontal line?
Answer:
0 = m

Question 100.
Find the angle between the lines x = 2 and y = 3.
Answer:
θ = 90°.

Question 101.
Write the slope of the line y = mx.
Answer:
‘m’

Question 102.
The midpoint of the line joining the points (1, 2) and (1, p) is (1, – 1), then find p.
Answer:
p = – 4.

Question 103.
Name the point of concurrence of me-dians of a triangle is called
Answer:
Centroid

Question 104.
If AC = AB + BC, then the points A, B, C are called points.
Answer:
Collinear

Question 105.
ax + by + c = 0, represents a
Answer:
Straight line

Question 106.
If the points (k, k), (2, 3) and (4, – 1) are collinear, then find k.
Answer:
\(\frac{7}{3}\) = k

Question 107.
Write other name for x-coordinate of a points.
Answer:
Abscissa

Question 108.
Find the slope of the line joining the points A(-1.4, – 3.7) and B(-2.4, 1.3).
Answer:
m = – 5

Question 109.
If a < 0, then (- a, – a) belongs to which quadrant ?
Answer:
Q1

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 110.
If θ is the angle made by a line with X – axis, then find slope’m’.
Answer:
m = tan θ

Question 111.
Find the area of square formed with the vertices (0, – 1), (2, 1), (0, 3) and (-2, 1) taken in order as vertices.
Answer:
∆ = 8 sq. units.

Question 112.
Name the person who was introduced coordinate geometry.
Answer:
Rene Descartes

Question 113.
Find the coordinates of centroid of the triangle formed with the vertices (-1,3), (6, -3) and (-3, 6).

Question 114.
In quadrilateral ABCD, AB = BC = CD = AD and \(\overline{\mathbf{A C}} \neq \overline{\mathbf{B D}}\), then it is Answer:……………..type of quadrilateral.
Answer:
Rhombus

Question 115.
Write the slope of the line joining the points (2a, 3b) and (a, – b).
Answer:
m = \(\frac{4 \mathrm{~b}}{\mathrm{a}}\)

Question 116.
Write a formula to distance of (x, y) from origin.
Answer:
\(\sqrt{x^{2}+y^{2}}\)

Question 117.
In rhombus all sides are……………….
Answer:
Equal in length.

Question 118.
If the slope of a line passing through (- 2, 3) and (4, a) is \(\frac { -5 }{ 3 }\), then find Answer:
Answer:
a = – 7.

119.
A(2a, 4a), B(2a, 6a), C(2a+ \(\sqrt{3}\), 5), then write ΔABC is a type of tri¬
angle.
Answer:
Equilateral triangle.

Question 120.
How much each angle in equilateral triangle ?
Answer:
60° = each angle.

Question 121.
In the below figure, G is the centroid then AG : GD = ………………
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 5
Answer:
2:1

Question 122.
In the below figure AD : GD =
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 6
Answer:
3 : 1

Question 123.
Write the midpoint of a line segment divides it in the ratio.
im
Answer:
1 : 1

Question 124.
If the distance between the points (x1, y1) and (x2, y2) is |x1 – x2|, then they are parallel to ……………..
Answer:
x-axis.

Question 125.
Find slope of the line joining the points A(0,0), B(1/2,1/2)
Answer:
1 = m

Question 126.
Write the equation of X – axis.
Answer:
Y = 0

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 127.
Write the point of concurrence of alti-tudes of a triangle is called ……………..
Answer:
Orthocentre

Question 128.
P(cos θ, – cos θ), Q (sin θ, sin θ), then find \(\overline{\mathbf{P Q}}\).
Answer:
\(\sqrt{2}\) units.

Question 129.
Diagonals in a parallelogram …………….. to each other.
Answer:
Bisect

Question 130.
Find slope of the line 3x – 2 = 0.
Answer:
Not defined = (\(\frac{0}{3}\))

Question 131.
If A(p, q), B(m, n) and C(p – m, q – n) are collinear, then find pn.
Answer:
qm

Question 132.
Write Y-axis can be represented as.
Answer:
X = 0

Question 133.
Write number of medians of a triangle.
Answer:
3

Question 134.
A(cot θ, 1), B(0, 0), then find \(\overline{\mathbf{B A}}\).
Answer:
cosec θ

Question 135.
If the point (4 – p) lie on X – axis, then find the value of p2 + 2p – 1.
Answer:
– 1

Question 136.
A(t, 2t), B(- 2, 6), C(3, 1) and ΔABC = 5 sq.units, then find ‘t’.
Answer:
t = 2

Question 137.
y-intercept of the line x – 2y + 1 = 0 is …………..
Answer:
b = \(\frac { 1 }{ 2 }\)

Question 138.
In the below figure find ‘x’.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 7
Answer:
-9 = x

Question 139.
In the below figure find ‘y’.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 8
Answer:
3 = y

Question 140.
Where the X and Y axes will inter¬sects ?
Answer:
(0, 0)

Question 141.
If the point (a, 5) lies on Y – axis find the value of ‘a’.
Answer:
a = 0.

Question 142.
Write (3, 0), (8, 0), (1/2, 0) points lie on ………….
Answer:
X – axis.

Question 143.
Nature of the line that does not pass through origin and having a zero slope is
Answer:
Parallel to X – axis.

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 144.
Y-intercept of the line y = mx + c is ….
Answer:
‘c’

Question 145.
In ΔABC, all the side are different, then it is called type of triangle.
Answer:
Scalene

Question 146.
A = (\(\frac{1}{2}, \frac{3}{2}\)) , B = (\(\frac{3}{2}, \frac{-1}{2}\)) then find \(\overline{\mathbf{B A}}\)
Answer:
\(\sqrt{5}\)

Question 147.
Find the area of below parallelogram, if ΔABC = 5 sq. units.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 9
Answer:
10 sq. units

Question 148.
Find x-intercept of the line x – y +1 =0.
Answer:
– 1

Question 149.
In ΔPQR, PQ = QR, then it is called ……………… triangle.
Answer:
Isosceles

Question 150.
If (1, x) is at \(\sqrt{10}\) units from origin, then find the value of ‘x’.
Answer:
x = ± 3

Question 151.
A(1, – 1), B(2 1/2, 0), C(4, 1), then find area of ΔABC.
Answer:
Δ = 0.

Question 152.
Name the line joining the mid point of one side of a triangle from opposite vertex is called …………….
Answer:
Median

Question 153.
Find angle made by the line y = x with the positive direction of X – axis.
Answer:
45°.

Choose the correct answer satistying the following statements.

Question 154.
Statement (A): The point (0, 4) lies on Y – axis.
Statement (B) : The X co-ordinate of the point on Y – axis zero.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 155.
Statement (A): The value of y is 6, for which the distance between the points P(2, – 3) and Q(10, y) is 10.
Statement (B): Distance between two given points A(x1, y1) and B(x2, y2) is given by
AB = \(\sqrt{\left(x_{2}+x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(iii)

Question 156.
Statement (A) : The point (- 1, 6) di¬vides the line segment joining the points (- 3, 10) and (6, – 8) in the ratio 2 : 7 internally.
Statement (B): Three points A, B and C are collinear if area of AABC = 0.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 157.
Statement (A) : Centroid of a triangle formed by the points (a, b), (b, c) and (c, a) is at origin, then a + b + c = 0.
Statement (B) : Centroid of a AABC with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is given by
\(\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 158.
Statement (A): The area of the triangle with vertices (- 5,-1), (3, – 5), (5, 2) is 32 square units.
Statement (B): The point (x, y) divides the line segment joining the points A(xj, y2) and B(x2, y2) in the ratio k : 1 externally, then
\(x=\frac{k x_{2}+x_{1}}{k+1}, y=\frac{k y_{2}+y_{1}}{k+1}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)

Question 159.
Statement (A): The ratio in which the segment joining the points (-3, 10) and (6, – 8) is divided by (- 1, 6) is 2 : 7.
Statement (B) : If A(x1, y1), B(x2, y2) are two points. Then the point C(x, y) such that C divides AB internally in the ratio k : 1 is given by
x = \(\frac{\mathrm{kx}_{2}+\mathrm{x}_{1}}{\mathrm{k}+1}, \mathrm{y}=\frac{\mathrm{ky}_{2}+\mathrm{y}_{1}}{\mathrm{k}+1}\)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 160.
Statement (A) : If three vertices of a parallelogram taken in order are (- 1, – 6), (2, – 5) and (7, 2), then its fourth vertex is (4, 1).
Statement (B) : Diagonals of a paral-lelogram bisect each other.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 161.
Statement (A) : The points (k -I- 1, 1), (2k + 1, 3) and (2k + 2, 2k) are col- linear, then k = 4.
Statement (B) : Three points A(x1, y1), B(x2, y2) and C(x3, y3) are collinear if and only if
x1(y2 – y3) + x2(y3-y1) + x3(y1-y2) = 0
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(iii)

Question 162.
Statement (A) : Let the vertices of a ΔABC are A(- 5, – 2), B(7, 6) and C(5, – 4), then coordinate of circum- centre is (1, 2).
Statement (B) : In a right angle tri¬angle, mid-point of hypotenuse is the circumcentre of the triangle.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 163.
Statement (A): If A(2a, 4a) and B(2a, 6a) are two vertices of a equilat¬eral triangle ABC, then the vertex C is given by (2a + a\(\sqrt{3}\) , 5a).
Statement (B): In equilaterahtriangle all the coordinates of three vertices can be rational.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)

Question 164.
Statement (A) : The equation of the straight line which passes through the point (2,-3) and the point of the inter-section of the lines x + y + 4 = 0 and 3x – y – 8 = 0 is 2x – y – 7 = 0.
Statement (B) : Product of slopes of two perpendicular straight lines is – 1.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Read Che below passages and answer to the following questions.

Let there be two points (4, 1) and (5,-2) in a two dimensional coordi¬nate system. A line which passes through the above give points and intersects the coordinate axes forms a triangle.

Question 165.
Write the equation of the line passing through the above given points.
Answer:
3x + y – 13 = 0.

Question 166.
Find the point of intersection of the above line with both the coordinate axes.
Answer:
(\(\frac { 13 }{ 3 }\),0) and (0, 13).

Question 167.
Find the area of the triangle so formed.
Answer:
\(\frac { 169 }{ 6 }\) sq. units.

In the diagram on a Lunar eclipse, if the position of Sun, Earth and Moon are shown by (- 4, 6) (k, – 2) and (5, – 6) respectively.

Question 168.
In Lunar eclipse what is the positions of Sun, Earth and Moon ?
Answer:
All are in same line, i.e., collinear.

Question 169.
To solve the above problem which mathematical concept is used ?
Answer:
Co-ordinate Geometry.

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 170.
Which formula is used to find the value of k ?
Δ = \(\frac { 1 }{ 2 }\) |x1(y2 – y3) + x2(y3-y1) + x3(y1 – y2) | = 0

Manowbhiram calculated the dis¬tance between T(5, 2) and R(-4, -1) to the nearest length is 9.5 units.

Question 171.
Do you agree with Manowbhiram ?
Answer:
Yes, I agree with him.

Question 172.
Which mathematical concept is used to you support Manowbhiram ?
Answer:
Co-ordinate Geometry (or) (Distance formula).

Question 173.
Column – II gives distance between pair of points given in column -I, match them correctly.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 10
Answer:
A – (iv), B – (i)

Question 174.
Column – II gives distance between pair of points given in column -I, match them correctly.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 11
Answer:
A – (ii), B – (iii)

Question 175.
Column – II gives the coordinates of the point ’p’ that divides the line segment join¬ing the points given in column -I, match them correctly.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 12
Answer:
A – (iv), B – (ii)

Question 176.
Column – II gives the coordinates of the point ‘p’ that divides the line segment join¬ing the points given in column -I, match them correctly.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 13
Answer:
A – (iii), B – (i).

Question 177.
Column – II gives the area of triangles whose vertices are given in column -1, match them correctly.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 14
Answer:
A – (iv), B – (iii).

Question 178.
Column – II gives the area of triangles whose vertices are given in column -1, match them correctly.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 15
Answer:
A – (ii), B – (i).

Question 179.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 16
Answer:
A – (iv), B – (iii).

Question 180.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 17
Answer:
A – (iii), B – (i).

AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers

Question 181.
Name the quadrilateral, which satis¬fies both the conditions given below.
Statement (A) : Diagonals are equal
Statement (B) : All sides are equal
a) Rhombus
b) Parallelogram
c) Rectangle
d) Square
Answer:
(d)

Question 182.
Find the area of the shaded triangle, in the figure given below.
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 18
Answer:
6 sq. units

Question 183.
What is the slope of the line joining the points (2, 0) and (- 2, 0).
Solution:
AP 10th Class Maths Bits Chapter 7 Coordinate Geometry with Answers 19

Question 184.
Name the point which is the point of intersection of medians of a triangle.
Answer:
Centroid of a triangle.