Question

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

Answer 1

Hope it will help you.............

Answer 2

Step-by-step explanation:

As per the question,

Three points are given as:

P(-2,2)

Q(2,2)

R(2,7)

Since we know that if these points are the vertices of right triangle, than it must follow Pythagoras Theorem. If ΔPQR is right angle triangle than

$PQ^{2}+QR^{2}=PR^{2}$

Formula used to find the distance of two points is given by:

$d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Now using this formula we can calculate the values of PQ², QR² and PR²

$QR^{2} = 16$

$PQ^{2} = 25$

$PR^{2} = 41$

Now,

$PQ^{2}+QR^{2}=PR^{2}$

$16+25=41$

That is LHS = RHS

Hence, proved.