In the coordinate plane, n passes through the points (-1,4) and (5,2) and m passes through the points (2,1) and (4,y). For what value of y is n perpendicular to m?

1 Answer
Jul 4, 2017

See the explanation below.

Explanation:

If two lines are perpendicular to each other, their slopes are opposite reciprocals.

To solve this problem, find the slope of line nn, find the slope that line mm should have, and then use the slope to figure out the point yy.

Slope of line nn:

m = (Deltax)/(Delta y) = (y_2-y_1)/(x_2-x_1) = (2-4)/(5-(-1)) = (-2)/6 = -1/3

The slope of line m is the opposite reciprocal of -1/3, which is 3.

Using the slope formula, substitute 3 in for the slope and calculate the value of y.

m = (Deltax)/(Delta y) = (y_2-y_1)/(x_2-x_1) = (y-1)/(4-2) = (y-1)/2

3 = (y-1)/2

6 = y-1

y = 7