Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.2

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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.2

9th Maths Coordinate Geometry Exercise 5.2 Question 1.
Find the distance between the following pairs of points.
(i) (1, 2) and (4, 3) Samacheer Kalvi 9th Maths Chapter 5 Coordinate Geometry Ex 5.2 1
(ii) (3, 4) and (- 7, 2)
(ii) (a, b) and (c, b)
(iv) (3, -9) and (-2, 3)
Solution:
We know that distance,
9th Maths Exercise 5.2 Solution Samacheer Kalvi
9th Maths Coordinate Geometry Exercise 5.2 Samacheer Kalvi

9th Samacheer Maths Solution Ex 5.2 Question 2.
Determine whether the given set of points in each case are collinear or not.
(i) (7, -2), (5, 1), (3, 4)
(ii) (a, -2), (a, 3), (a, 0)
Solution:
(i) Let the points be A (7, -2), B (5, 1) and C (3, 4). By the distance formula.
9th Maths Exercise 5.2 Samacheer Kalvi
∴ Hence the points are collinear.

(ii) Let the points be A (a, -2), B (a, 3) and C (a, 0).
9th Class Maths Exercise 5.2 Solution Samacheer Kalvi
∴ Hence the points are collinear.

Chapter 5 Coordinate Geometry Answers Question 3.
Show that the following points taken in order form an isosceles triangle.
(i) A (5, 4), B(2, 0), C (-2, 3)
(ii) A (6, -4),B (-2, -4), C (2, 10)
Solution:
(i) Let the points be A (5, 4), B (2, 0) and C (-2, 3)
Class 9 Maths Exercise 5.2 Solution Samacheer Kalvi
Exercise 5.2 Class 9 Samacheer Kalvi
Here AB + BC > CA and AB = BC. ∴ ∆ ABC is an isosceles triangle.

(ii) Let the points be A (6, -4), B (-2, -4) and C (2, 10).
9th Maths 5.2 Samacheer Kalvi
Here BC + BA > CA and BC = CA. Two sides are equal, so ∆ ABC is an isosceles triangle

Coordinate Geometry Solutions Ex 5.2 Question 4.
Show that the following points taken in order form an equilateral triangle in each case.
(i) A(2, 2), B(-2, -2), C(\(-2 \sqrt{3}\), \(2 \sqrt{3}\))
(ii) A(\(\sqrt{3}\) ,2), B (0, 1), C(0, 3)
Solution:
(i) Let the points be A (2, 2) B (-2, -2) and C(\(-2 \sqrt{3}\), \(2 \sqrt{3}\))
Maths Class 9 Chapter 5 Exercise 5.2 Samacheer Kalvi
All the 3 sides of ∆ABC are equal, Hence ∆ABC is an equilateral triangle.

(ii) Let the points be A (\(\sqrt{3}\), 2), B (0, 1) and C (0, 3).
Exercise 5.2 9th Class Samacheer KalviAll the 3 sides of ∆ABC are equal. Hence ∆ABC is an equilateral triangle.

Class 9 Maths Exercise 5.2 Solution Question 5.
Show that the following points taken in order form the vertices of a parallelogram.
(i) A(-3, 1), B(-6, -7), C (3, -9) and D(6, -1)
(ii) A (-7, -3), B(5, 10), C(15, 8) and D(3, -5)
Solution:
(i) Let A, B, C and D represent the points (-3, 1), (-6, -7) (3, -9) and (6, -1) respectively.
Exercise 5.2 Class 10 Samacheer Kalvi
The opposite sides are equal. Hence ABCD is a parallelogram.

(ii) Let A, B, C and D represent the points (-7, -3), (5, 10) (15, 8) and (3, -5)
9th Std Maths Exercise 5.2 Samacheer Kalvi
The opposite sides are equal. Hence ABCD is a parallelogram.

Exercise 5.2 Class 9 Question 6.
Verify that the following points taken in order form the vertices of a rhombus.
(i) A(3, -2), B (7, 6),C (-1, 2) and D (-5, -6)
(ii) A (1, 1), B(2, 1),C (2, 2) and D(1, 2)
Solution:
(i) Let the points be A(3, -2), B (7, 6), C (-1, 2) and D (-5, -6)
9th Class Math Ex 5.2 Solution Samacheer Kalvi
Samacheer Kalvi 9th Maths Book Answers Ex 5.2∴ All the four sides of quadrilateral ABCD are equal. Hence ABCD is a rhombus.

9th Maths 5.2 Question 7.
If A(-1, 1), B(1, 3) and C(3, a) are points and if AB = BC, then find ‘a’
Solution:
Exercise 5.2 Class 9 Solutions Samacheer Kalvi

Maths Solutions For Class 9 Samacheer Kalvi Ex 5.2 Question 8.
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, what are the coordinates of A?
Solution:
9th Maths 5.2 Exercise Samacheer Kalvi
Class 9 Maths Chapter 5 Exercise 5.2 Samacheer Kalvi
Co-ordinates of A are (-5, -5) or (9, 9)

9th Maths Book Ex 5.2 Question 9.
The point (x, y) is equidistant from the points (3, 4) and (-5, 6). Find a relation between x and y.
Solution:
P(x, y) is equidistant from the points A(3, 4) and B(-5, 6)
Ex 5.2 Class 9 Samacheer Kalvi

Geometry 5.2  9th Maths Ex 5.2 Question 10.
Let A(2, 3) and B(2, -4) be two points. If P lies on the x-axis, such that AP = \(\frac{3}{7}\)AB, find the coordinates of P.
Solution:
Ex5.2 Class 9 Samacheer Kalvi

9th Maths Guide Ex 5.2 Question 11.
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, -4) and (5, -6)
Solution:
Class 9th Maths Chapter 5 Exercise 5.2 Samacheer Kalvi
9 Maths Samacheer Kalvi Exercise 5.2
Therefore S is the centre of the circle, passing through A, B and C.

5 Coordinate Geometry Ex 5.2 Question 12.
The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.
Solution:
9th Class Math 5.2 Exercise Solution Samacheer Kalvi