You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

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) 9th Maths Exercise 5.2 Samacheer Kalvi Chapter 5 Coordinate Geometry
(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 Chapter 5 Coordinate Geometry
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 5.2 Exercise Samacheer Kalvi Chapter 5 Coordinate Geometry
∴ Hence the points are collinear.

(ii) Let the points be A (a, -2), B (a, 3) and C (a, 0).
9th Maths 5.2 Samacheer Kalvi Chapter 5 Coordinate Geometry
∴ 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)
9th Std Maths Exercise 5.2 Samacheer Kalvi Chapter 5 Coordinate Geometry
9th Maths Exercise 5.2 Samacheer Kalvi Chapter 5 Coordinate Geometry
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 Standard Maths Exercise 5.2 Samacheer Kalvi Chapter 5 Coordinate Geometry
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(\(-2 \sqrt{3}\), \(2 \sqrt{3}\))
9th Maths Ex 5.2 Samacheer Kalvi Chapter 5 Coordinate Geometry
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).
Ex 5.2 Class 9 Samacheer Kalvi Chapter 5 Coordinate GeometryAll the 3 sides of ∆ABC are equal. Hence ∆ABC is an equilateral triangle.

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.
9th Class Maths Exercise 5.2 Solution Samacheer Kalvi Coordinate Geometry
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)
Class 9 Maths Exercise 5.2 Solution Samacheer Kalvi Chapter 5 Coordinate Geometry
The opposite sides are equal. Hence ABCD is a parallelogram.

Form 3 Maths Exercise 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)
Exercise 5.2 Class 9 Samacheer Kalvi Chapter 5 Coordinate Geometry
Samacheer Kalvi 9th Maths Exercise 5.2 Chapter 5 Coordinate Geometry∴ All the four sides of quadrilateral ABCD are equal. Hence ABCD is a rhombus.

Question 7.
If A(-1, 1), B(1, 3) and C(3, a) are points and if AB = BC, then find ‘a’
Solution:
10th Maths Exercise 5.2 Samacheer Kalvi Chapter 5 Coordinate Geometry

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 Exercise 5.2 In Tamil Samacheer Kalvi Chapter 5 Coordinate Geometry
Coordinate Geometry Class 9 Exercise 5.2 Samacheer Kalvi Chapter 5
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)
Exercise 5.2 Class 9 Samacheer Kalvi Chapter 5 Coordinate Geometry

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:
Class 9th Maths Chapter 5 Exercise 5.2 Samacheer Kalvi Coordinate Geometry

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:
Exercise 5.2 Class 9 Solutions Samacheer Kalvi Chapter 5 Coordinate Geometry
Exercise 5.2 9th Class Chapter 5 Coordinate Geometry Samacheer Kalvi
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:
Samacheer Kalvi 9th Maths Book Answers Samacheer Kalvi Chapter 5 Coordinate Geometry

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