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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.5

Question 1.

Find the centroid of the triangle whose vertices are

(i) (2, -4 ), (-3, -7) and (7, 2)

(ii) (-5, -5), (1, -4) and (-4, -2)

Solution:

Question 2.

If the centroid of a triangle is at (4,-2) and two of its vertices are (3, -2) and (5, 2) then find the third vertex of the triangle.

Solution:

Centroid G (x, y) = (4, -2)

Question 3.

Find the length of median through Aof a triangle whose vertices are A(-1, 3), B(1, -1) and C(5, 1).

Solution:

Question 4.

The vertices of a triangle are (1, 2), (h, -3) and (-4, k). If the centroid of the triangle is at the point (5, -1) then find the value of \(\sqrt{(h+k)^{2}+(h+3 k)^{2}}\)

Solution:

Question 5.

Orthocentre and centroid of a triangle are A(-3, 5) and B(3, 3) respectively. If C is the circumcentre and AC is the diameter of this circle, then find the radius of the circle.

Solution:

Question 6.

ABC is a triangle whose vertices are A(3, 4), B(-2, -1) and C(5, 3). If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.

Solution:

∴ The co-ordinates of the vertex D(x, y) = (1, 0)

Question 7.

If \(\) \(\) and \(\) are mid points of the sides of a triangle, then find the centroid of the triangle.

Solution:

“The centroid of the triangle obtained by joining the mid points of the sides of a triangle is the same as the centroid of the original triangle.”

∴ The mid points of the sides of the triangle are given as