Question

Find the third vertex of a triangle if its two vertices are A (-1, 4) and B (5, 2) and mid- point of one side is (0, 3)

• A. (1, 2)
• B. (-5, 4)
• C. Both A & B
• D. None of these

Answer 1

The correct option is C

Both A & B

Let the third vertex be C (x, y)

If (0, 3) is mid- point of BC then $\left(\frac{x+5}{2}\right)=0$ (or) x = - 5, $\left(\frac{y+2}{2}\right)=3$, y=4.

(x, y) = (-5, 4)

If (0, 3) is midpoint of AC then $\left(\frac{x-1}{2}\right)=0$, x=1

$\left(\frac{y+4}{2}\right)=3$, y + 4 = 6, y = 2

(x, y) = (1, 2)

$\therefore$ (-5, 4) and (1, 2) are possible answers.