Answer:
y = -2/3x - 11
Step-by-step explanation:
Steps to find the perpendicular bisector:
1) Find the midpoint of line PQ
Midpoint formula: ([tex]\frac{x_{1} + x_{2} }{2} \\[/tex], [tex]\frac{y_{1} + y_{2}}{2}[/tex])
Midpoint of line PQ = (6, -2)
2) Find the slope of line PQ
Slope formula: [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
Slope of line PQ = 3/2
3) Find the negative reciprocal of the slope of PQ
To find the negative reciprocal just swap the numerator and denominator and add a negative sign. If it is already negative it will become positive.
In this case it will be -2/3
4) Write the equation of line PQ in slop-intercept form.
Slope-intercept form: y = mx + b
This is what it will look like for line PQ: y = [tex]\frac{3}{2}[/tex]x + b
5) Plug the points of the midpoint into the line and solve for the intercept (b)
This is what it will look like: -2 = [tex]\frac{3}{2}[/tex](6) + b
-2 = 18/2 + b
-2 = 9 + b
-11 = b
6) Write the equation of the perpendicular bisector
m = the negative reciprocal of the slope of PQ = -2/3
This is what the equation will look like: y = -2/3x - 11
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