Question

Two vertices of a triangle are (3, -5) and (-7, 4). If the centroid of the triangle is (2, -1), then the coordinates of the third vertex are .

• A. (10, -2)
• B. (-10, -2)
• C. (10, 2)
• D. (-10, 2)

Answer 1

The correct option is A (10, -2)

Let the coordinates of the third vertex be (x, y).
$\therefore \frac{x+3-7}{3}=2\mathrm{and}\frac{y-5+4}{3}=-1\Rightarrow x-4=6\mathrm{and}y-1=-3\Rightarrow x=10\mathrm{and}y=-2\mathrm{Hence},\mathrm{the}\mathrm{coordinates}\mathrm{of}\mathrm{the}\mathrm{third}\mathrm{vertex}\mathrm{are}\left(10,-2\right).$