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

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

Correct Answer: Option C

Explanation

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

Midpoint = ((frac{2 + (-5)}{2}, frac{-3 + 1}{2}))

= ((frac{-3}{2}, -1))

Slope of the line PQ = (frac{1 – (-3)}{-5 – 2})

= (-frac{4}{7})

The slope of the perpendicular line to PQ = (frac{-1}{-frac{4}{7}})

= (frac{7}{4})

The equation of the perpendicular line: (y = frac{7}{4}x + b)

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

(-1 = (frac{7}{4})(frac{-3}{2}) + b)

(-1 + frac{21}{8} = frac{13}{8} = b)

(therefore) 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)

There is an explanation video available below.