AP 9th Class Maths Chapter 3 Co-Ordinate Geometry Important Questions

These AP 9th Class Maths Important Questions 3rd Lesson Co-Ordinate Geometry will help students prepare well for the exams.

AP Board Class 9 Maths 3rd Lesson Co-Ordinate Geometry Important Questions

9th Class Maths Co-Ordinate Geometry 2 Marks Important Questions

Question 1.
Define origin.
Solution:
We draw two number lines perpendicular to each other in a plane. The horizontal number line X’X is known as X – axis. The vertical number line Y’Y is known as Y – axis. The intersecting point of X – axis and Y – axis is called origin. We denote origin with ‘O’.

Question 2.
Describe the position of the point P(3, 4).
Solution:
The x – coordinate is 3 and y-coordinate is 4. The point P is at a distance of 3 units from Y – axis measured along positive X – axis and it is at a distance of 4 units from X – axis measured along positive Y – axis.

Question 3.
In which quadrant or on which axis does each of the following points lie? (4, 0), (-4, 2), (3, -2), (3, 4), (-4, -5), (0, -3)?
Solution:
The point (4, 0) lies on x-axis.
The point (-4, 2) lies in II-quadrant.
The point (3, -2) lies in IV-quadrant.
The point (3, 4) lies in I-quadrant.
The point (-4, -5) lies in III-quadrant.
The point (0, -3) lies on y-axis.

Question 4.
The locations of various activities at an amusement park are shown. Write the coordinates of the points.
a) Food court
b) Space ride
c) Park entrance
d) Water ride

Solution:
a) Food court → (-8, 6)
b) Space ride → (6, 2)
c) Park entrance → (-10, -8)
d) Water ride → (2, -2)

Question 5.
In the given figure of a circle, write the coordinates of the points where circle meets the axes.

Solution:
Let the circle meet OX at A and OX’ at A’.
Then,
A → (4, 0)
A’ → (-4, 0)
Let the circle meet OY at B and OY’ at B’.
Then,
B → (0, 4)
B’ → (0, -4)

Question 6.
Write coordinates of two points on x – axis and two points on y-axis which are at equal distances from the origin.
Solution:
The coordinates of two points on x-axis which are at equal distances from the origin can be taken as (1, 0) and (-1, 0).

The coordinates of two points on y- axis which are at equal distances from the origin can be taken as (0, 1) and (0,-1).

Question 7.
Plot the point P(-5, 1) and from it draw PM and PN perpendiculars to x-axis and y- axis respectively. Write the coordinates of M and N.
Solution:

M → (-5, 0)
N → (0, 1)

Question 8.
Plot A (3, – 2) on a Cartesian plane.
Solution:

Question 9.
Plot three points A(4, 0), B(0, -4) and C(-4, 0) on the coordinate plane. Now, plot point D so that ABCD is a rhombus. Give coordinates of the point D.
Solution:

9th Class Maths Co-Ordinate Geometry 4 Marks Important Questions

Question 1.
In which quadrant or on which axis do each of the points (-2, 4), (3, -1), (-1, 0), (1, 2) and (-3, -5) lie ? Verify your answer by locating them on the Cartesian plane.
Solution:
The point (-2, 4) lies in the II quadrant.
The point (3, -1) lies in the IV quadrant.
The point (-1, 0) lies on the negative x-axis.
The point (1, 2) lies in the I quadrant.
The point (-3, -5) lies in the III quadrant.

Question 2.
Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

Solution:

Question 3.
Write the coordinates of the points A, B, C, D, E and F in the following graph.

Solution:
A → (2, 4) B → (0, 4)
C → (-3, 2) D → (-2, 0)
E → (-4, -2) F → (3, -2)

Question 4.
From the graph, find the coordinates of the points A, B, C, D, E and F. Which points have same abscissa? Also, find which points have same ordinates.

Solution:
A → (0, -3) B → (4, -5)
C → (6, 3) D → (4, 5)
E → (-6, 3) F → (3, 0)
The points B and D have same abscissa.
The points C and E have same ordinates.

Question 5.
Plot the points on graph paper A(2, 0), B(6, 0) and C(4, 6) in order. Find the area of Δ ABC.
Solution:

Area of Δ ABC = \(\frac{\text { Base } \times \text { Height }}{2}\) = \(\frac{4 \times 6}{2}\) = 12 square units

Question 6.
In a cartesian system, whether the points (3, 5) and (5, 3) are same ? Justify.
Solution:
Given points A(3, 5), B(5, 3) are not same.

The positions are not the same.
∴ The points are not same.

Question 7.
Write the Co-ordinates of the vertices of a Trapezium DEFG.

Solution:
Vertices of a trapezium DEFG are D(1, 3), E(5, 3), F(7, -1), G(1,-1).

Question 8.
Observe the adjacent figure, answer the following :
a) Coordinates of points A and B.
b) Distance between A and C.
c) Distance between B and C.
d) ABC is a _________ triangle.

Solution:
a) A(1, 5), B(4, 0)
b) 5 units
c) 3 units
d) Right angle triangle

Question 9.
Observe the graph below and answer the questions that follow :

(i) In the above figure, coordinates of points in second quadrant are
A) (-3, 2) and (-2, 3)
B) (3, 2) and (2, 3)
C) (3, -2) and (-2, – 3)
D) (-3, -2) and (-2, -3)
Answer:
A) (-3, 2) and (-2, 3)

(ii) In the above figure, coordinates of points in third quadrant are
A) (-3, 2) and (-2, 3)
B) (3, 2) and (2, 3)
C) (3, -2) and (-2, -3)
D) (-3, -2) and (-2, -3)
Answer:
D) (-3, -2) and (-2, -3)

(iii) In the above figure, coordinates of points in fourth quadrant are
A) (-3, 2) and (-2, 3)
B) (3, 2) and (2, 3)
C) (3, -2) and (2, -3)
D) (-3, -2) and (-2, -3)
Answer:
C) (3, -2) and (2, -3)

(iv) In the above figure, coordinates of points on y-axis are
A) (-4, 0) and (3, 0)
B) (4, 0) and (-3, 0)
C) (0, -4) and (0, 3)
D) (0, 4) and (0, -3)
Answer:
C) (0, -4) and (0, 3)

(v) In the above figure, coordinates of points on X-axis are
A) (-4, 0) and (3, 0)
B) (4, 0) and (-3, 0)
C) (0, -4) and (0, 3)
D) (0, 4) and (0, -3)
Answer:
A) (-4, 0) and (3, 0)

9th Class Maths Co-Ordinate Geometry 8 Marks Important Questions

Question 1.
On the x-axis, plot four points such that the distance between any two consecutive points is equal.
(OR)
Write coordinates of four points on x-axis such that the distance between two consecutive points is the same.
Solution:
Let us plot the points A(1, 0), B(2, 0), C(3, 0) and D(4, 0) on x-axis. Then, we find that AB = BC = CD = 1 unit.

Question 2.
Plot the points P(0, -4) and Q(0, 4) on the graph paper. Now, plot the points R and S so that Δ PQR and Δ PQS are isosceles triangles. How many isosceles triangles can be formed ?
Solution:

Let us plot the points R(1, 0), S (2, 0).
Then,
PR² = OP² + OR² (By Pythagoras Theorem)
= (4)² + (1)² = 16 + 1 = 17 ⇒ PR = \(\sqrt{17}\)
QR² = OQ² + OR² (By Pythagoras Theorem)
= (4)² + (1)² = 16 + 1 = 17
⇒ QR = \(\sqrt{17}\)
∴ PR = QR
∴ ΔPQR is isosceles.
Similarly, we can prove that Δ PQS is an isosceles triangle.
We can draw infinitely many isosceles triangles by taking countless points on X’OX.

Question 3.
Locate the points (2, 0), (5, 4), (0, 4), (-3, 2), (-2, -3), (0, -3), (2,-3) on cartesian plane in your answer sheet.
Solution:

Question 4.
Plot the following points on a graph paper.
(2, 3), (-2, 4), (-3, -3), (7, 3), (3, 0), (0, 4), (-5, 0), (0, 0)
Solution:

Question 5.
From the following table answer the given questions below.

i) The point belongs to Q₃
Solution:
N(-3, -3)

ii) Abscissa of point Q
Solution:
-7

iii) Suin of the abscissa and ordinate of point L
Solution:
1

iv) The point lies on X-axis
Solution:
O(0, 0) or M(5, 0)

v) Distance between point R and X-axis
Solution:
2 units

vi) The point lies on Y-axis
Solution:
O(0, 0) or S (0, 8)

vii) The point belongs to both the axes
Solution:
O(0, 0)

viii) Ordinate of point S
Solution:
8

AP 9th Class Maths Important Questions Chapter 3 The Elements of Geometry

Question 1.
Write converse of the theorem “In ΔABC, if AB = AC then C = ∠B”.
Solution:
In ΔABC, ∠C = ∠B then AB = AC.

Question 2.
Write converse of the theorem “In ΔABC, if AB = AC then ∠C = ∠B”.
Solution:
In ΔABC, ∠C = ∠B then AB = AC.

Question 3.
Write any two Euclid’s postulates.
Solution:
i) There is a unique line that passes through the given two distinct points.
ii) We can draw a circle with any centre and radius.

Question 4.
Write any two Euclid’s axioms.
Solution:
i) Things which are equal to the same things are equal to one another.
ii) Things which coincide with one another are equal to one another.
iii) The whole is greater than the part.

Question 5.
If x + a is a common factor of f(x) = x² + x – 6 and g(x) = x² + 3x – 18, then find the value of a.
Solution:
given polynomials are f(x) = x² + x – 6 and g(x) = x² + 3x – 18
f(x) and g(x) having common factors (x + a), So
x + a = 0 ⇒ x = -a
f(-a) = (-a)²+ (-a) – 6
= a² – a – 6
g(-a) = (-a)² + 3(-a) – 18
= a² – 3a – 18
f(-a) = g(-a)
a² – a – 6 = a² – 3a – 18
a² – a² – a + 3a = -18 + 6
2a = -12
a = -6.

Question 6.
If a + b = 5 and a² + b² = 11,then prove that a³ + b³ = 20
Solution:
Given a + b = 5 and
a² + b² = 11
(a + b)² = (5)²
a² + b² + 2ab = 25
11 + 2ab = 25
2ab = 14
ab = 7
a³ + b³ = (a + b) (a² + b² – ab)
= 5(11 – 7)
= 5 × 4 = 20
∴ a³ + b³ = 20.

Question 7.
Disprove that “a² > b² for all a > b” by . finding a suitable counter example.
Solution:
If a > b so,
Let a = 3 and b = 2
a² = 3² and b² = 2²
9 > 4 so,
∴ If a > b, then a² > b².

Question 8.
Explain Euclid’s 5^thpostulate with the help of a diagram.
Solution:
Euclid’s 5th postulate : If a straight line , falling on two straight lines makes the interior angles on the same side of it taken together is less than two right angles, then the two straight lines, if produced infinitely, meet on that side on \frhich the sum of the angles is less than two right angles.

The lines AB and CD will intersect on left side of PQ.