Practice the AP 10th Class Maths Bits with Answers Chapter 7 Coordinate Geometry on a regular basis so that you can attempt exams with utmost confidence.

## 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)

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)

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), (x_{1}, y_{1}) points.

Answer:

\(\sqrt{\mathrm{x}_{1}^{2}+\mathrm{y}_{1}^{2}}\)

Question 21.

If A(log_{2} 8, log_{5} 25) and B(log_{10} 10, log_{10} 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.

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.

Answer:

3 sq. units.

Question 31.

Find the slope of the line that passes through the points P (x_{1}, y_{1}) and Q(x_{2}, y_{2}) 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.

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 (x_{1}, y_{1}) and (x_{2}, y_{2}) which are on the line parallel to Y – axis.

Answer:

|y – y_{2}| or |y_{2 }– y_{1} |

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.

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:

Q_{4}

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:

Q_{2}

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 a^{3} + b^{3} + c^{3}.

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(x_{1}, y_{1}) and Q(x_{2}, y_{2}).

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

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 (x_{1}, y_{1}) and (x_{2}, y_{2}) 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)

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:

Q_{1}

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 = ………………

Answer:

2:1

Question 122.

In the below figure AD : GD =

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 (x_{1}, y_{1}) and (x_{2}, y_{2}) is |x_{1} – x_{2}|, 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

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 p^{2} + 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’.

Answer:

-9 = x

Question 139.

In the below figure find ‘y’.

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.

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.

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(x_{1}, y_{1}) and B(x_{2}, y_{2}) 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(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) 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)

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(x_{1}, y_{1}), B(x_{2}, y_{2}) 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(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) are collinear if and only if

x_{1}(y_{2} – y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) = 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.

Question 170.

Which formula is used to find the value of k ?

Δ = \(\frac { 1 }{ 2 }\) |x_{1}(y_{2} – y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1} – y_{2}) | = 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.

Answer:

A – (iv), B – (i)

Question 174.

Column – II gives distance between pair of points given in column -I, match them correctly.

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.

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.

Answer:

A – (iii), B – (i).

Question 177.

Column – II gives the area of triangles whose vertices are given in column -1, match them correctly.

Answer:

A – (iv), B – (iii).

Question 178.

Column – II gives the area of triangles whose vertices are given in column -1, match them correctly.

Answer:

A – (ii), B – (i).

Question 179.

Answer:

A – (iv), B – (iii).

Question 180.

Answer:

A – (iii), B – (i).

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.

Answer:

6 sq. units

Question 183.

What is the slope of the line joining the points (2, 0) and (- 2, 0).

Solution:

Question 184.

Name the point which is the point of intersection of medians of a triangle.

Answer:

Centroid of a triangle.