Answer:
y = -3/4x - 33/4
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!