Question

The points $(0,7,10),(-1,6,6)$ and $(-4,9,6)$ form

• A. a right angled isosceles triangle
• B. a scalene triangle
• C. a right angled triangle
• D. an equilateral triangle

Answer 1

Answer: (A)

Let $P(0,7,10),Q(-1,6,6)$ and $R(-4,9,6)$ be the vertices of a triangle
Here, $PQ=\sqrt{1+1+16}=3\sqrt{2}$
$QR=\sqrt{9+9+0}=3\sqrt{2}$
$PR=\sqrt{16+4+16}=6$
Now, $P{Q}^2+Q{R}^2=(3\sqrt{2}{)}^2+(3\sqrt{2}{)}^2=36=(PR{)}^2$
Therefore, $\Delta PQR$ is a right angled triangle at $Q$. Also, $OQ$ $=$ OR. Hence, $\Delta PQR$ is a right angled isosceles triangle.