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)
8y + 14x + 13 = 0
8y - 14x + 13 = 0
8y - 14x - 13 = 0
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)−5−2
= −47
The slope of the perpendicular line to PQ = −1−47
= 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
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