Question

3. A line segment whose endpoints are (3,9) and (7,k) is perpendicular to a line whose slope is --2. Which

of the following is the value of k?
(1) 1
(3) 11
(2) -7
(4) -5

Answer 1

(3) 11

Explanation:

A line perpendicular to one with a slope of -2 will have the opposite reciprocal slope: -1/(-2) = 1/2.

The point-slope equation of the line through (3, 9) with slope 1/2 is ...

y -9 = 1/2(x -3)

Then for point (7, k) on the line we have ...

k -9 = 1/2(7 -3)

k = 9 +2 = 11

The value of k is 11.