Question

Find the coordinates of circumcentre of ΔPQR where P ≡ (6, −5), Q ≡ (6, 7), R ≡ (8, 7).

Answer 1

To find the coordinates of the circumcentre of triangle ΔPQR where:

P = (6,−5)

Q = (6, 7)

R = (8, 7)

Identify that triangle PQR is a right triangle:

Observe the coordinates:

PQ is vertical: same x-coordinate (6), so vertical line.

QR is horizontal: same y-coordinate (7), so a horizontal line.

∴ ∠PQR = 90°

In a right-angled triangle, the circumcentre is the midpoint of the hypotenuse.

2. Find the hypotenuse

The hypotenuse is the side opposite the right angle, which is PR.

P = (6, −5)

R = (8, 7)

Find the midpoint of PR

Use midpoint formula:

Midpoint = `(x_1 + x_2)/2, (y_1 + y2)/2`

= `(6 + 8)/2, (−5 + 7)/2`

= (7, 1)