Question

Janet draws triangle PQR with vertices P(1,), Q(-2,4), and R(1,7) she claims that the triangle is an isosceles right triangle which statement shows that Janet is correct

Answer 1

First note P must be (1,1). Compute slopes and distances:

Slope PQ = (4−1)/(−2−1) = 3/(−3) = −1.
Slope QR = (7−4)/(1−(−2)) = 3/3 = 1.
Since (−1)(1) = −1, PQ ⟂ QR.

Distance PQ = sqrt[(-3)^2 + 3^2] = sqrt(18).
Distance QR = sqrt[3^2 + 3^2] = sqrt(18).
So PQ = QR.

Thus PQ = QR and PQ ⟂ QR, so triangle PQR is an isosceles right triangle (right angle at Q).