Question

Two vertices of a \(\triangle \mathrm{ABC}\) are \(\mathrm{A}(-1,4)\) and \(\mathrm{B}(5, 2)\) and its centroid is (0, –3). The coordinates of C are ______.

Options

• (4, 3)

• (4, 15)

• (–4, –15)

• (–15, –4)

Answer 1

Two vertices of a \(\triangle \mathrm{ABC}\) are \(\mathrm{A}(-1,4)\) and \(\mathrm{B}(5, 2)\) and its centroid is (0, –3). The coordinates of C are (–4, –15).

Explanation:

Using \(\frac{-1 + 5 + x_C}{3} = 0\)

\(\Rightarrow x_C = -4\)

And \(\frac{4 + 2 + y_C}{3} = -3\)

\(\Rightarrow y_C = -15\) 

Hence \(C(-4, -15)\).