SOLUTION: Please help me with this problem. Find a general form of an equation for the perpendicular bisector of the segment AB. A (4,-3) B (-2,5) (Answer) = -1

Algebra ->  Points-lines-and-rays -> SOLUTION: Please help me with this problem. Find a general form of an equation for the perpendicular bisector of the segment AB. A (4,-3) B (-2,5) (Answer) = -1      Log On


   

Question 996413: Please help me with this problem.
Find a general form of an equation for the perpendicular bisector of the segment AB.
A (4,-3) B (-2,5)
(Answer) = -1
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A (4,-3) , B (-2,5)
The slope of Find the negative reciprocal of the slope of line AB, because
a line with such slope will be perpendicular to line AB.

m%5Bp%5D=-%28%284-%28-2%29%29%2F%28-3-5%29%29
-%28%286%29%2F%28-8%29%29
6%2F8
highlight_green%283%2F4%29

Bisector must pass through the midpoint of line AB.
system%28x=%284-2%29%2F2=1%2Cy=%28-3-5%29%2F2=-4%29
Midpoint being (1,-4).

Find the line of slope 3%2F4 and containing point (1,-4).


RESULT: highlight%28y=%283%2F4%29x-19%2F4%29

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YOU ASKED FOR GENERAL FORM EQUATION OF THE LINE, SAME AS SLOPE-INTERCEPT FORM, SAME AS FUNCTION FORM. THAT IS THE FORM OF THE ANSWER WHICH I GAVE. If you want a different form than that, then YOU change it!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me with this problem.
Find a general form of an equation for the perpendicular bisector of the segment AB.
A (4,-3) B (-2,5)
(Answer) = -1
Slope of line AB: -+4%2F3

Slope of perpendicular bisector: 3%2F4

Line of the perpendicular bisector will intersect AB at its midpoint, or coordinate point: (1, 1)

With m, or slope = 3%2F4, and point (1, 1), equation of perpendicular bisector to AB is: y+-+y%5B1%5D+=+m%28x+=+x%5B1%5D%29 ------> y+-+1+=+%283%2F4%29%28x+-+1%29 -------> y+-+1+=+%283%2F4%29x+-+3%2F4

4y+-+4+=+3x+-+3  ------ Multiplying by LCD, 4

3x - 4y - 3 + 4 = 0 --------> highlight_green%283x+-+4y+%2B+1+=+0%29