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 5.3

Question 1.

Find the mid-points of the line segment joining the points

(i) (-2, 3) and (-6, -5)

(ii) (8, -2) and (-8, 0)

(iii) (a, b) and (a + 2b, 2a – b)

(iv) \(\left(\frac{1}{2},-\frac{3}{7}\right)\) and \(\left(\frac{3}{2}, \frac{-11}{7}\right)\)

Solution:

Question 2.

The centre of a circle is (-4, 2). If one end of the diameter of the circle is (-3, 7) then find the other end.

Solution:

∴ The other end is (-5, -3)

Question 3.

If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0, then

what will be the value of p?

Solution:

Question 4.

The midpoint of the sides of a triangle are (2, 4), (-2, 3) and (5, 2). Find the coordinates of the vertices of the triangle.

Solution:

Question 5.

O(0, 0) is the centre of a circle whose one chord is AB, where the points A and B are (8, 6) and (10, 0) respectively. OD is the perpendicular from the centre to the chord AB. Find the coordinates of the mid-point of OD.

Solution:

Question 6.

The points A (-5, 4), B (-1, -2) and C(5, 2) are the vertices of an isosceles right¬angled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square.

Solution:

Question 7.

The points A(-3, 6), B(0, 7) and C(1, 9) are the mid points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallelogram.

Solution:

In a parallelogram diagonals bisect each other and diagonals are not equal.

Question 8.

A (-3, 2), B (3, 2) and C(-3, -2)are the vertices of the right triangle, right angled at A. Show that the mid point of the hypotenuse is equidistant from the vertices.

Solution:

Hence proved