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?

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Answer 1 · 2017-07-04T19:30:14

See the explanation below.

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

To solve this problem, find the slope of line #n#, find the slope that line #m# should have, and then use the slope to figure out the point #y#.

Slope of line #n#:

#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#