Find the equation of the line that passes through (−2,1) and is perpendicular to the line that passes through the following points: (5,2),(−12,5)

Stephany Wilkins

Stephany Wilkins

Answered question

2022-10-13

Find the equation of the line that passes through (−2,1) and is perpendicular to the line that passes through the following points: (5,2),(−12,5)

Answer & Explanation

Shyla Maldonado

Shyla Maldonado

Beginner2022-10-14Added 15 answers

The slope of the line joining points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by y 2 - y 1 ( x 2 - x 1 ) . Hence slope of line joining (5,2) and (−12,5) is 5 - 2 - 12 - 5 = - 3 17
Hence slope of the line perpendicular to line joining (5,2) and (−12,5) will be - 1 - 3 17 or 17 3 , as product of slopes of lines perpendicular to each other is −1.
Hence equation of line passing through (−2,1) and having slope 17 3 will be (using point-slope form)
( y - 1 ) = 17 3 ( x - ( - 2 ) ) or 3 ( y - 1 ) = 17 ( x + 2 ) ) or
17 x - 3 y + 37 = 0

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