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

Given P(-2, 2), Q(2, 2) and R(2, 7).
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
By distance formula , distance between two points = √[(x₂-x₁)²+(y₂-y₁)²]
PQ = √[(2-(-2))²+(2-2)²]
PQ = √[(4²+0²]
PQ = √16
PQ = 4 …..(i)
QR = √[(2-2)²+(7-2)²]
QR = √[(0)²+(5)²]
QR = √25
QR = 5 …….(ii)
PR = √[(2-(-2))²+(7-2)²]
PR = √[4²+5²]
PR = √16+25
PR = √41…….(iii)
PQ²+QR² = 4²+5²
= 16+25
=41
PR² = 41
PQ²+QR² = PR²
PQR is a right triangle.
P,Q,R are the vertices of a right angled triangle.