SOLUTION: Find the equation of the line perpendicular to 2x+3y=1 and whose distance from the origin is 7. Please include solutions if you can. Thank you!

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line perpendicular to 2x+3y=1 and whose distance from the origin is 7. Please include solutions if you can. Thank you!      Log On


   

Question 1172332: Find the equation of the line perpendicular to 2x+3y=1 and whose distance from the origin is 7. Please include solutions if you can. Thank you!
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Here are a few hints.

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Hint 1)

Any standard linear equation of the form
Ax+By = C
is perpendicular to
Bx-Ay = D

I've swapped the A and B coefficients, and made the plus sign into a minus sign. We use a new value D so that it's different from C.

In the case of 2x+3y = 1, we have
A = 2
B = 3
C = 1

Anything perpendicular to 2x+3y = 1 looks like
Bx-Ay = D
3x-2y = D

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Hint 2)


Refer to this diagram

We have the blue line as 2x+3y = 1
The red line 2x+3y = 0 is parallel to the blue one. This red line goes through the origin, which helps us find point P.

The green line is perpendicular to the red line, and it is one of the answers. It goes through point P. Note how point P is 7 units away from the center point O.
Segment OP = 7 units
Similarly, OQ = 7 units as well.

You'll have to use x%5E2%2By%5E2=49 and 2x%2B3y=0 to determine the coordinates of P and Q. So you'll get two possible answers. Once you know the coordinates of P, you plug them into 3x-2y=D to determine the value of D. Do the same for the coordinates of Q

Note: the diagram above shows only one of the two solutions. The other solution is the same idea but it goes through Q instead.