**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 (x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3});

then the centroid is given by:

Since given that the centroid is (0,0)

∴ for x coordinate: = 0

∴ X_{1} + X_{2 }+ X_{3 }= 0

∴ (- 8) + (9) + x_{ }= 0

∴ X + 1_{ }= 0

**∴ X = – 1**

Similarly, for y coordinate: = 0

∴ Y_{1} + Y_{2 }+ Y_{3 }= 0

∴ (7) + (4) + Y_{ }= 0

∴ Y + 11_{ }= 0

**∴ Y = – 11**

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