Question

If $\left(P\right(2,2),Q(2,6)$ and $R(-2,4)$ are the vertices of a triangle then $\Delta$PQR is

• A. Equilateral
• B. Scalene
• C. Isosceles
• D. Right angle

Answer 1

Answer: (C)

Isosceles

$PQ=\sqrt{{(2-2)}^2+{(6-2)}^2}=\sqrt{0+16}=4$
$QR=\sqrt{{(-2-2)}^2+{(4-6)}^2}=\sqrt{16+4}=\sqrt{20}$
$PR=\sqrt{{(-2-2)}^2+{(4-2)}^2}=\sqrt{16+4}=\sqrt{20}$
We see that $PR=QR$
The triangle is isosceles.