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

Algebra ->  Finance -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Two lines
L1 : 2y-3x-6=0
L2 : 3y%2Bx-20=0+
intersect at point A
find the coordinates of the intersection point
2y-3x-6=0.......solve for y
2y=3x%2B6
y=%283%2F2%29x%2B3.........eq.1
3y%2Bx-20=0+
3y=-x%2B20+
y=-%281%2F3%29x%2B20%2F3+........eq.2
from eq.1 and eq.2 we have
+%283%2F2%29x%2B3=-%281%2F3%29x%2B20%2F3+......solve for x
+%283%2F2%29x%2B%281%2F3%29x=20%2F3+-3
+%2811x%29%2F6=11%2F3
+11x=6%2811%2F3%29
+11x=2%2811%29
+x=2%2811%29%2F11
+x=2
go to
y=%283%2F2%29x%2B3.........eq.1, substitute x
y=%283%2F2%292%2B3
y=3%2B3
y=6
=> point A=(2,6)

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 y=-%281%2F3%29x%2B20%2F3+; so, slope is -1%2F3
negative reciprocal is -1%2F%28-1%2F3%29=3
=> a slope of the line L3 is 3
to find the equation of L3, use a slope point formula
y-y%5B1%5D=m%28x-x%5B1%5D%29 .....plug in a slope and coordinates of the point A
y-6=3%28x-2%29
y-6=3x-6
y=3x-6%2B6
y=3x+->answer






Answer by Alan3354(69443) About Me  (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
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Find the coordinates of point A.
Find the slope of L2, call it m1.
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The slope of lines perpendicular to L2 have a slope of -1/m1, call it m.
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Use y-y1 = m(x - x1) where (x1,y1) is point A.
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I don't need the practice.
This is basic, know it.