Question

6(a)(i) Two vertices of a triangle are (-4,6) and (2,-2) and its centroid is (0,3). Find the coordinate of thirdVertex​

Answer 1

Answer:(0,0)

Step-by-step explanation:

Answer 2

The coordinate of the third vertex is (2,5).

• The two vertices of the triangle are given as (-4,6) and (2,-2).
• Centroid of the triangle is given as (0,3)
• 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

0 = $\frac{-4 + 2 + x_3}{3}$

x = 2

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

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

y = 5

• The coordinates of the third vector is (2,5).