Question

Prove that P(−1, 0), Q(1, 3) and R(5, 9) are collinear.

Answer 1

Given:

Points P(−1, 0), Q(1, 3), and R(5, 9).

Calculate the slope of PQ:

\[\text{slope}_{PQ} = \frac{y_2 - y_1}{x_2 - x_1}\]

= \[\frac{3 - 0}{1 - (-1)}\]

= \[\frac{3}{2}\]

Calculate the slope of QR:

\[\text{slope}_{QR} = \frac{9 - 3}{5 - 1}\]

= \[\frac{6}{4}\]

= \[\frac{3}{2}\]

Slop PQ = slop QR = `3/2`, the points P, Q, and R lie on the same straight line.

Therefore, P(−1, 0), Q(1, 3), and R(5, 9) are collinear.