Find the slope of the line perpendicular to the line passing through the points (3, 5) and (−4, 2).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(-\frac{7}{3}\)
Two lines are perpendicular when the product of their slopes is −1, so the required slope is the negative reciprocal of the slope of the line through the two given points.
Slope of the line through (3, 5) and (−4, 2) is the change in y over the change in x: \(\displaystyle m=\frac{2-5}{-4-3}=\frac{3}{7}\)
Slope of the perpendicular line is the negative reciprocal: \(\displaystyle -\frac{1}{m}=-\frac{7}{3}\)