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 ->  Points-lines-and-rays -> 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 1172331: 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!
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The left side of an equation of a line PARALLEL to a given line Ax+By=C has
the same left side Ax+By but a different number for C on the right.

The left side of an equation of a line PERPENDICULAR to a given line Ax+By=C
has the left side Bx-Ay but a different number for C on the right.

So a line perpendicular to 2x+3y=1 has left side 3x-2y. Let's say it's right
side is a number C.

Then we use the formula

Distance from the point (x1,y1)
to the line Ax+By+C=0 is

d = abs%28Ax%5B1%5D%2BBy%5B1%5D%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29

abs%283%280%29-2%280%29%2BC%29%2Fsqrt%28%283%29%5E2%2B%28-2%29%5E2%29=7

abs%28C%2Fsqrt%289%2B4%29%29=7

abs%28C%2Fsqrt%2813%29%29=7

abs%28C%29=7sqrt%2814%29

C=+%22%22+%2B-+7sqrt%2814%29

So there are two solutions:

3x-2y=+%22%22+%2B-+7sqrt%2814%29

The given line is:



Here is the first line 3x-2y=+7sqrt%2814%29 in red.
The green line to the origin is 7 units long:




Here is the second line 3x-2y=+-7sqrt%2814%29, also in red.
The green line to the origin is also 7 units long:



Edwin

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

The correct answer is THIS 

    There are two solutions (two straight lines)

        3x - 2y = +/- 7%2Asqrt%2813%29.