Question

If g(-2 1) is the centroid of a triangle abc and two of its vertices are a(1,-6) and b(-5,2),find the third vertex of the triangle

Answer 1

The coordinate of the third vertex is (-2,7).

• The two vertices of the triangle are given as (1,-6) and (-5,2).
• Centroid of the triangle is given as (-2,1)
• The formula to find the centroid of the triangle is given by

C(x,y) = ($\frac{x_{1}+x_{2}+x_{3} }{3}$,$\frac{y_{1}+y_{2}+y_{3} }{3}$)

where (x,y) are the points of the centroid and (x₁,y₁),(x₂,y₂) and (x₃,y₃) are the points of the triangle.

• Substituting the known values we solve for x- coordinate of the third vertex

-2 = $\frac{1 + (-5) + x_3}{3}$

x = -2

• Now calculating for y-coordinate of the third vertex of triangle

1 = $\frac{-6 + 2 + y_{3}}{3}$

y = 7

• The coordinates of the third vector is (-2,7).