SOLUTION: Find the equation of the line that is perpendicular to the line segment from (-3, 4) to (1, -2) and passes through the line segment at its midpoint. I'm not sure how to do t

Question 72641: Find the equation of the line that is perpendicular to the line
segment from (-3, 4) to (1, -2) and passes through the line segment
at its midpoint.
I'm not sure how to do the line when it is perpendicular, please help!
ThAnKs!
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
The slope is the key here.
Thus slope =(y2-y1)/(x2-x1)
(-2-4)/(1+3)
-6/4
-3/2 this is the slope through the 2 points.
the line equation here is:
4=-3/2*-3+b
4=9/2+b
b=4-9/2
b=4-4.5
b=-.5
thus the equation for this line is y=-3x/2-.5
the perpendicular line has a slope that is the negative reciprical of this slope. Thus:
this slope =2/3. the mid point of the line through (-3,4)(1,-2) is:
mid point of x=(1+3)2=4/2=2 or -3+2=-1 or 1-2=-1 so the x value is x=-1
mid point of y=(2+4)/2=6/2=3 or 4-3=1 or -2+3=1 so the midpoint is y=1
now we have a point & the slope thus the line equation is:
Y=mX+b
1=2/3*-1+b
1=-2/3+b
b=1-2/3
b=1/3 therefore the equation is:
y=2/3x+1/3
(graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = 2x/3 +1/3 and y = -3x/2 -.5 ).

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