SOLUTION: Two lines L1 :2y-3x-6=0and L2 :3y+x-20=0 intersect at point A. A third line L3 is perpendicular to L2 at point A. Find the equation of L3

Question 1189115: Two lines L1 :2y-3x-6=0and L2 :3y+x-20=0 intersect at point A. A third line L3 is perpendicular to L2 at point A. Find the equation of L3
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Two lines
L1 :
L2 :
intersect at point A
find the coordinates of the intersection point
.......solve for

.........eq.1

........eq.2
from eq.1 and eq.2 we have
......solve for

go to
.........eq.1, substitute

=> point A=(,)

A third line L3 is perpendicular to L2 at point A.
perpendicular lines have slopes negative reciprocal to each other
line L2 in slope intercept form is ; so, slope is
negative reciprocal is
=> a slope of the line L3 is
to find the equation of L3, use a slope point formula
.....plug in a slope and coordinates of the point A

->answer

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Two lines L1 :2y-3x-6=0and L2 :3y+x-20=0 intersect at point A. A third line L3 is perpendicular to L2 at point A. Find the equation of L3
-------------
Find the coordinates of point A.
Find the slope of L2, call it m1.
=========
The slope of lines perpendicular to L2 have a slope of -1/m1, call it m.
-----
Use y-y1 = m(x - x1) where (x1,y1) is point A.
-------------------------------------------------------
I don't need the practice.
This is basic, know it.
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