Q) Two vertices of a triangle have coordinates (-8,7) and (9,4). If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?

Ans: Given that two vertices of a triangle are (-8,7) and (9,4); Centroid is (0,0)

Let the third vertex be (X, Y)

We know that if a triangle has 3 coordinates as (x₁, y₁), (x₂, y₂), (x₃, y₃);

then the centroid is given by: 

Since given that the centroid is (0,0)

∴ for x coordinate: = 0

∴ X₁ + X₂ + X₃ = 0

∴ (- 8) + (9) + x = 0

∴ X + 1 = 0

∴ X = – 1

Similarly, for y coordinate: = 0

∴ Y₁ + Y₂ + Y₃ = 0

∴ (7) + (4) + Y = 0

∴ Y + 11 = 0

∴ Y = – 11

Therefore, the coordinates of third vertex are (-1, -11)