Question

Do the points P (1, 0), Q (−5, 0) and R (−2, 5) form a triangle? If so, name the type of triangle formed.

Answer 1

Given: P (1, 0), Q (−5, 0) and R (−2, 5)

Formula: The distance formula (d) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

PQ = `sqrt((-5 - 1)^2 + (0 - 0)^3)`

= `sqrt((-6)^2 + 0^2)`

= `sqrt(36 + 0)`

= `sqrt36`

= 6

QP = `sqrt([-5 - (-2)]^2 + (0 - 5)^2)`

= `sqrt((-5 + 2)^2 + (0 - 5)^2)`

= `sqrt((-3)^2 + 25)`

= `sqrt(9 + 25)`

= `sqrt(34)`

PR = `sqrt((-2 - 1)^2 + (5 - 0)^2)`

= `sqrt((-3)^2 + 5^2)`

= `sqrt(9 + 25)`

= `sqrt(34)`

∴ QR = PR

PQR is an isosceles triangle.