Find the 3 vertex of a traingle if two of its vertex are at

Question

(-2,4) and (7,-3) and the centroid at (3,2)?

Answer 1

The two vertices of triangle are (-2, 4) and (7, -3).

Centroid of triangle is (3, 2)

Let required vertex of traingle is (x₃, y₃).

(x₁, y₁) = (-2, 4), (x₂, y₂) = (7, - 3)

Formula for the centroid of triangle = [(x₁ + x₂ + x₃)/3 , (y₁+ y₂ + y₃)/3]

(3, 2) = [(- 2 + 7 + x₃)/3 , (4 - 3 + y₃)/3]

(3, 2) = [(5 + x₃)/3 , (1 + y₃)/3]

(5 + x₃)/3 =  3

5 + x₃ = 3 * 3

5 + x₃ = 9

 x₃ = 9 - 5

 x₃ = 4

(1 + y₃)/3 = 2

1 + y₃ = 2 * 3

1 + y₃ = 6

 y₃ = 6 - 1

y₃ = 5

Remaining vertex of triangle = (4, 5).