Find the equation of the line that is perpendicular to the line passing through (5,12) and (6,14) at midpoint of the two points

beefypy

beefypy

Answered question

2022-10-13

Find the equation of the line that is perpendicular to the line passing through (5,12) and (6,14) at midpoint of the two points

Answer & Explanation

pararevisarii

pararevisarii

Beginner2022-10-14Added 9 answers

First, we need to find the slope of the original line from the two points.
y 2 - y 1 x 2 - x 1
Plugging in corresponding values yields:
14 - 12 6 - 5
= 2 1
=2
Since the slopes of perpendicular lines are negative reciprocals of each other, the slope of the lines we’re looking for is going to be the reciprocal of 2, which is - 1 2
Now we need to find the midpoint of those two points, which will give us the remaining information to write the equation of the line.
The midpoint formula is:
( x 1 + x 2 2    ,    y 1 + y 2 2 )
Plugging in yields:
( 5 + 6 2    ,    12 + 14 2 )
= ( 11 2 , 13 )
Therefore, the line we’re trying to find teh equation of passes through that point.
Knowing the slope of the line, as well as a point where it passes through, we can write its equation in point-slope form, denoted by:
y - y 1 = m ( x - x 1 )
Plugging in yields:
y - 13 = - 1 2 ( x - 11 2 )

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