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 ofAB=(8−6)4−(−2)=26=13 m2=slope ofCD=(24−12)(x−8)=12(x−8)
Now, AB⊥CD⇒m1m2=−1 ⇒13×12(x−8)=−1 ⇒−x+8=4⇒x=4