Question

A(3, 1), B(y, 4) and C(1, x) are vertices of triangle ABC and G(3, 4) is its centroid. Find the values of x and y. Also, find the length of side BC.

Answer 1

Since, G(4, 3) is the centroid of ΔABC, we have

`(3 + y + 1)/3 = 3` and `(1 + 4 + x)/3 = 4`

`=>` 4 + y = 9 and 5 + x = 12

`=>` y = 5 and x = 7

Hence, the values of x and y are x = 7 and y = 5.

The coordinates of the point B and C are (5, 4) and (1, 7) respectively.

Length of side BC = `sqrt((1 - 5)^2 + (7 - 4)^2`

= `sqrt((-4)^2 + (3)^2`

= `sqrt(16 + 9)`

= `sqrt(25)`

= 5 units