SOLUTION: write an equation in slope-intercept form (y=mx+b) for the perpendicular bisector of the segment between (3,4) and (-2,5)...please show all steps

Question 631600: write an equation in slope-intercept form (y=mx+b) for the perpendicular bisector of the segment between (3,4) and (-2,5)...please show all steps
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
(3,4) and (-2,5)
The equation for this line is to be determined.
x1 y1 x2 y2
3 4 -2 5

slope m = (y2-y1)/(x2-x1)
( 5 - 4 )/( -2 - 3 )
( 1 / -5 )
m= - 1/ 5

Find theco-ordinates of the mid point (3,4) and (-2,5)

(3-2)/2 = 0.5
(4+5)/2 = 4.5
The co-ordinates of the mid point are (0.5,4.5)
Equation of line perpendicular to the line joining (3,4) and (-2,5)and passing through (0.5,4.5)
Equation of line joining the points
y = - 1/ 5 x + 23/5
Divide by 1
y = - 1/ 5 x + 23/5
Compare this equation with y=mx+b,
m= slope & b= y intercept
slope m = - 1/5

The slope of a line perpendicular to the above line will be the negative reciprocal.
Because m1*m2 =-1
The slope of the required line will be 5

m= 5 ,point ( 0.5 , 4.5 )
Find b by plugging the values of m & the point in
y=mx+b
4.5 = 5/ 2 + b
b= 2
m= 5
The required equation is y=5x+2
m.ananth@hotmail.ca

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