Question

Without using the distance formula, show that the points A(4, −2), B(−4, 4) and C(10, 6) are the vertices of a right-angled triangle.

Answer 1

The given points are A(4, −2), B(−4, 4) and C(10, 6).

Slope of AB = `(4 + 2)/(-4 - 4)`

Slope of AB = `6/(-8)`

Slope of AB = `(-3)/4`   ...(1)

Slope of BC = `(6 - 4)/(10 + 4)`

Slope of BC = `2/14`

Slope of BC = `1/7`  ...(2)

Slope of AC = `(6 + 2)/(10 - 4)`

Slope of AC = `8/6`

Slope of AC = `4/3`  ...(3)

From (1) and (3)

It can be seen that:

Slope of AB = `(-1)/"Slope of AC"`

Hence, AB ⊥ AC

Thus, the given points are the vertices of a right-angled triangle.