Find an equation for the perpendicular bisector of the line segment whose endpoints are ( − 2 , 7 ).and ( − 8 , − 3 ).

Answer 1

a line through (-2,7) and (-8,-3) has slope =

(7--3)/(-2--8) = 10/6 = 5/3

perpendicular lines have the negative inverse slope = -3/5

change the sign and flip the fraction upside down

y=mx + b

y=-3x/5 + b

plug in the midpoint to calculate b, the midpoint is the average of the coordinates: (-5, 2)

average x coordinate = (-2-8)/2 = -10/2 =-5

average y coordinate = (7-3)/2 = 4/2 = 2

2 =-3(-5)/5 + b

b = 2-3 =-1

the perpendicular line has the equation

y=-3x/5 -1

or

5y =-3x -5

or

3x +5y +-5

It may help to plot the points and and graph the lines

even a rough sketch can help.

Answer 2

Hello Fhima.

Since we have bisector, that meas we will find a midpoint first;

If you refer the formula (you just get an average of x and y vertices)

So, our midpoint is; (-2+-8)/2 , (7 +-3)/2 = (-5, 2).

Since it is perpendicular; product of their slope is -1; slope of given line is: (7- -3)/(-2 - -8) = 10/6 = 5/3

product of their slope is -1; 5/3 * m. = -1 then m = -3/5

We have a line with slope -3/5 and one point (-5, 2)

when you use point-slope formula;

y - 2 = -3/5 *(x - -5)

y -2 = -3x/5 -3

y = -3x/5 -1

hope that helps