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Find the equation of the perpendicular bisector of the li...

Find the equation of the perpendicular bisector of the line joining P(2, -3) to Q(-5, 1)

A.

8y + 14x + 13 = 0

B.

8y - 14x + 13 = 0

C.

8y - 14x - 13 = 0

D.

8y + 14x - 13 = 0

Correct answer is C

Given P(2, -3) and Q(-5, 1)

Midpoint = (2+(5)2,3+12)

= (32,1)

Slope of the line PQ = 1(3)52

= 47

The slope of the perpendicular line to PQ = 147

= 74

The equation of the perpendicular line: y=74x+b

Using a point on the line (in this case, the midpoint) to find the value of b (the intercept).

1=(74)(32)+b

1+218=138=b

The equation of the perpendicular bisector of the line PQ is y = \frac{7}{4}x + \frac{13}{8}

\equiv 8y = 14x + 13 \implies 8y - 14x - 13 = 0