Question

In ΔPQR, ∠R = 90°, P = (8, −7), Q = (2, 1) and QR = 8 units. Find the length of the PQ and PR.

Answer 1

∠R = 90°

P(8, −7)

Q(2, 1)

QR = 8 units

We need PQ and PR.

Step 1: Find PQ using distance formula

PQ = `sqrt((x_2 − x_1)^2 + (y_2 − y_1))`

PQ = `sqrt((2 − 8)^2 + (1 − (−7))^2)`

PQ = `sqrt((−6)^2 + (8)^2)`

PQ = `sqrt(36 + 64)`

PQ = `sqrt100`

PQ = 10 units

Step 2: Use Pythagoras Theorem

Since △PQR is right-angled at R:

PQ² = PR² + QR²

10² = PR² + 64

PR² = 36

PR = 6