The points (−1, 3), (2, p) and (5, −5) lie on one straight line. Using the fact that the triangle they form must have zero area, what is the value of p?

Set the area expression to zero: ½|$x$₁$(y$₂ − $y$₃) + $x$₂$(y$₃ − $y$₁) + $x$₃$(y$₁ − $y$₂)| = ½|$(-1)(p+5)+2(-5-3)+5(3-p)$| = ½|$-p-5-16+15-5p$| = ½|$-6p-6$| = 0, so $p=-1$. Check with slopes: from (−1, 3) to (5, −5) the slope is −8/6 = −4/3, and from (−1, 3) to (2, −1) it is −4/3 as well.