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Question 1180511: Find the equation of the line which passes through point (1,1) and is perpendicular to line AB which passes through points A(1,-2) and B(5,6).
Note: Can you please show the full solution? Thank you!
Found 3 solutions by Boreal, mananth, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The slope of AB is 8/4 or 2
The slope of a perpendicular line to AB has slope which is the negative reciprocal of 2, or -1/2.
That line goes through point (1, 1).
Its equation is y-y1=m(x-x1) where m is slope and (x1, y1) point.
y-1=-(1/2)(x-1)
y=-(1/2)x+(3/2)
-
the other line using the point slope formula is y-6=2(x-5), or y=2x-4
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website!
Find the equation of the line which passes through point (1,1) and is perpendicular to line AB which passes through points A(1,-2) and B(5,6).
Equation of AB
x1 y1 x2 y2
1 -2 5 6
slope m = (y2-y1)/(x2-x1)
( 6 - -2 )/( 5 - 1 )
( 8 / 4 )
m= 2.00
Plug value of the slope and point ( 1 , -2 ) in
Y = m x + b
-2.00 = 2 + b
b= -2.00 - 2
b= -4
So the equation of AB will be
Y = 2 x -4
slope of the line = 2
The slope of a line perpendicular to the above line will be the negative reciprocal
m1*m2=-1
The slope of the required line will be 0.50
m= 1/2 ,point ( 1 , 1 )
Find b by plugging the values of m & the point in -0.875
y=mx+b
2 = 1.75 + b
b= 0.25
m= -0.875
The required equation is y = - 7/8 x+ 1/4
Answer by ikleyn(52786)  (Show Source):
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