Question

If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

Answer 1

Letbe ant triangle such that P (−2, 3); Q (4,−3) and R (4, 5) are the mid-points of the sides AB, BC, CA respectively.

We have to find the co-ordinates of the centroid of the triangle.

Let the vertices of the triangle be

In general to find the mid-point of two pointsand we use section formula as,

So, co-ordinates of P,

Equate the x component on both the sides to get,

…… (1)

Similarly,

…… (2)

Similarly, co-ordinates of Q,

Equate the x component on both the sides to get,

…… (3)

Similarly,

…… (4)

Similarly, co-ordinates of R,

Equate the x component on both the sides to get,

…… (5)

Similarly,

…… (6)

Add equation (1) (3) and (5) to get,

Similarly, add equation (2) (4) and (6) to get,

We know that the co-ordinates of the centroid G of a triangle whose vertices are is-

So, centroid G of a triangle is,