Find the equation of the perpendicular bisector of the line that passes through the points (-9, -14) and (3, 2).
Plz show work and explain

y = -3/4x - 33/4

Step-by-step explanation:

Find the line that passes through these two points:

Slope (m): y2-y1/x2-x1

m = 2-(-14)/3-(-9)

m = 16/12

m=4/3

so, the equation is y = 4/3x + b, with b being the y-intercept we need to find by substituting a point from the line, (3, 2):

y = 4/3x + b

2 = 4/3(3) + b

2 = 4 + b

b = -2

so, the equation is y = 4/3x - 2

now, we need to find the equation of the perpendicular bisector, which is a line that passes through the line segment at the midpoint and at a 90 degree angle:

so, the midpoint of the line segment of the line y = 4/3x - 2 is:

M = (x1+x2/2, y1+y2/2) <-- Midpoint Formula

M = (-9+3/2, -14+2/2)

M = (-3, -6)

the slope of this perpendicular bisector is equation to the negated inverse (-1/m) of the slope of the line segment:

m1 = 4/3

m = -3/4

so, the equation is y = -3/4x + b, find the y-intercept using the midpoint:

y = -3/4x + b

-6 = -3/4(-3) + b

b = -33/4

so the equation of the perpendicular bisector is y = -3/4x - 33/4.

Hope this helps and have a nice day!