Question

Two vertices of ΔАBC are A(–1, 4) and B(5, 2) and its centroid is G(0, –3). Then, the coordinates of C are ______.

Options

• (4, 3)

• (4, 15)

• (–4, –15)

• (–15, –4)

Answer 1

Two vertices of ΔАBC are A(–1, 4) and B(5, 2) and its centroid is G(0, –3). Then, the coordinates of C are (–4, –15).

Explanation:

The centroid G of triangle ABC is `((x_A + x_B + x_C)/3, (y_A + y_B + y_C)/3)`.

Using A(–1, 4), B(5, 2) and G(0, –3) gives

x: (–1) + 5 + x_C = 3 × 0 

⇒ 4 + x_C = 0

⇒ x_C = –4

y: 4 + 2 + y_C = 3 × (–3) 

⇒ 6 + y_C = –9

⇒ y_C = –15

So, C = (–4, –15).