SOLUTION: What is the equations of the line passing through (8,−2) and perpendicular to the line whose equation is x−7y−9=0
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Question 1092180: What is the equations of the line passing through (8,−2) and perpendicular to the line whose equation is x−7y−9=0
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Find the slope of the given line
----------------------
Any line perpendicular to this line has
slope where
---------------------
(8,-2)
Use the general point-slope formula
----------------------
check:
Does the line go through ( 8, -2 ) ?
OK
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Here is a much faster way to find the answer to a problem like this. It uses something called a dot product that you will learn about when you study vectors. The key is this:
Given a line with equation
(where c can be any constant)
the equation of any line perpendicular to the given line will have an equation of the form
(where d can be any constant)
Notice that the coefficients on x and y have changed places, and one of them has changed sign.
So in your problem, given the equation
the equation of any line perpendicular to the given line is of the form
Then, since you know the coordinates of one point on the line, (8,-2), you can determine the value of c in the equation.
So the equation of the line perpendicular to the given line and passing through the given point is
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