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?

Jadon Johnson

Jadon Johnson

Answered question

2022-11-08

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?

Answer & Explanation

hoatryearnenizts

hoatryearnenizts

Beginner2022-11-09Added 10 answers

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 = Δ x Δ 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 = Δ x Δ 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

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