Question

Verify that points P(-2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled
triangle.​

Answer 1

Answer:

Yes, it is a right-angle triangle.

Step-by-step explanation:

As shown in the attachment, there is a right angle, so it is a right-angle triangle.

Answer 2

Answer:

∠Q is right angle

Step-by-step explanation:

$A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\\overrightarrow{AB}=<x_B-x_A,\ y_B-y_A>$

$\overrightarrow{v}=<a,\ b>,\ \overrightarrow{q}=<c,\ d>\\\\\overrightarrow{v}\circ\overrightarrow{q}=ac+bd\\\\\text{If}\ \overrightarrow{v}\perp\overrightarrow{q}\ \text{then}\ \overrightarrow{v}\circ\overrightarrow{q}=0$

We have

$P(-2,\ 2);\ Q(2,\ 2);\ R(2,\ 7)\\\\\overrightarrow{PQ}=<2-(-2),\ 2-2>=<4,\ 0>\\\\\overrightarrow{PR}=<2-(-2),\ 7-2>=<4,\ 5>\\\\\overrightarrow{QR}=<2-2,\ 7-2>=<0,\ 5>$

$\overrightarrow{PQ}\circ\overrightarrow{PR}=4\cdot4+0\cdot5=16\neq0\\\\\overrightarrow{PQ}\circ\overrightarrow{QR}=4\cdot0+0\cdot5=0$