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Question
What is the slope of a line perpendicular to the line joining A(5, 1) and P where P is the mid-point of the segment joining (4, 2) and (–6, 4).
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Solution
Mid-point of XY = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
= `((4 - 6)/2, (2 + 4)/2)`
= `((-2)/2, 6/2)`
= `(– 1, 3)`
Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`
= `(3 - 1)/(-1 - 5)`
= `(2)/(-6)`
= `(-1)/3`
Slope of the line ⊥' to AP = `(-1)/"slope of AP"`
= `(-1)/(-1/3)`
= 3
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