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Question

If the line through the points (2,6) and (4,8) is perpendicular to the line through the points (8,12) and (x,24), then the value of x is

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Solution

Let A(2,6),B(4,8),C(8,12) and D(x,24) be the given points.
Let m1 and m2 be the slopes of AB and CD respectively. Then,
m1= slope of AB=(86)4(2)=26=13
m2= slope of CD=(2412)(x8)=12(x8)
Now, ABCDm1m2=1
13×12(x8)=1
x+8=4x=4

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