Question

Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle. 

Answer 1

In a right angles triangle ABC, right-angled at B, according to the Pythagoras theorem

AB² + BC² = AC²

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by

`d = root(2)((a - c)^2 + (b - d)^2`....(1)

For the given points Distance between P and Q is

PQ = `sqrt((-2-2)^2 + (2 - 2)^2) = sqrt(16)`

QR = `sqrt((2-2)^2 + (7 - 2)^2) = sqrt(25)`

PR = `sqrt((-2-2)^2 + (2 - 7)^2) = sqrt(16 + 25) = sqrt(41)`

PQ² = 16

QR² = 25

PR² = 41

As PQ² + QR² = PR²

Hence the given points form a right-angled triangle.