Find the value of p for which the points (-2, 5), (-5, -10) and (p, -13) are collinear.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-\frac{28}{5}\)
Three points are collinear when they lie on one straight line, so the slope between any two pairs of them is the same.
Slope through (−2, 5) and (−5, −10): \(\displaystyle \frac{-10-5}{-5+2}=\frac{-15}{-3}=5\)
Slope through (−5, −10) and (p, −13): \(\displaystyle \frac{-13+10}{p+5}=\frac{-3}{p+5}\)
\(\displaystyle \frac{-3}{p+5}=5\), so \(5p+25=-3\)
\(5p=-28\), so \(p=-\frac{28}{5}\)