For what value of \(x\) are the points A (−3, 12), B (7, 6) and C (x, 9) collinear.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Three points are collinear when they lie on one straight line. A straight line has the same slope everywhere, so the points are collinear when the slope from A to B equals the slope from A to C.
Slope of AB, the rise over the run from A to B: \(\displaystyle\frac{6-12}{7-(-3)}=\frac{-6}{10}=-\frac{3}{5}\)
Slope of AC, in the same way: \(\displaystyle\frac{9-12}{x-(-3)}=\frac{-3}{x+3}\)
Making the two slopes equal: \(\displaystyle\frac{-3}{x+3}=-\frac{3}{5}\) gives \(x+3=5\), so \(x=2\)
