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Find the equation of the line that is perpendicular to \(2y ...

Find the equation of the line that is perpendicular to 2y+5x6=0 and bisects the line joining the points P(4, 3) and Q(-6, 1)

A.

y + 5x + 3 = 0

B.

2y - 5x - 9 = 0

C.

5y + 2x - 8 = 0

D.

5y - 2x - 12 = 0

Correct answer is D

Line:2y+5x6=0

2y=65xy=35x2

Gradient = 52

For the line perpendicular to the given line, Gradient = 152=25

The midpoint of P(4, 3) and Q(-6, 1) = (6+42,3+12)

= (-1, 2).

Therefore, the line = y2x+1=25

2(x+1)=5(y2)5y2x12=0