Question

The slope of the line passing through points (x1, y1) and (X2, y2) is found
y2 - y1
X2 - X1

The line passing through the points (1, 2) and (x, 5) is perpendicular to
. What is the value of x ?

A

B

C

D

using the formula

a line that has a slope of

3

10

-2

-4

0

Answer 1

Slope of the line through (1,2) and (x,5) is m1 = (5−2)/(x−1) = 3/(x−1).

If that line is perpendicular to a line with slope m2, then m1·m2 = −1, so
3/(x−1) · m2 = −1 ⇒ x − 1 = −3m2 ⇒ x = 1 − 3m2.

For the given slopes:
- m2 = 3 ⇒ x = 1 − 9 = −8
- m2 = 10 ⇒ x = 1 − 30 = −29
- m2 = −2 ⇒ x = 1 − (−6) = 7
- m2 = −4 ⇒ x = 1 − (−12) = 13
- m2 = 0 ⇒ x = 1 − 0 = 1 (this corresponds to a vertical line x = 1, since a line perpendicular to a horizontal line is vertical)

If you tell me which slope (choice A–E) is the one referenced, I can state the single correct x.