Question

Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.

Answer 1

PQ = `sqrt((5 - 0)^2 + (10 - 5)^2`
= `sqrt(25+25)`
= `sqrt(50)`
= 5`sqrt(2)`

QR = `sqrt((6 - 5)^2 + (3 - 10)^2`
= `sqrt(1+49)`
= `sqrt(50)`
= 5`sqrt(2)`

RP = `sqrt((0 - 6)^2 + (5 - 3)^2`
= `sqrt(36+4)`
= `sqrt(40)`
= 2`sqrt(10)`

Since, PQ = QR, ΔPQR is an isosceles triangle.