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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (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%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y+=+2x%2F3+%2B1%2F3%2C+y+=+-3x%2F2+-.5%29+ (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 ).