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Question

If the point A is symmetric to the point B(4, –1) with respect to the bisector of the first quadrant, then the length of AB is

A

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B

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C

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D

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Solution

The correct option is B Let A ≡ (a, b) The coordinates of the midpoint C of AB are (a+42,b−12). Since it lies on the line y = x (the bisector of first quadrant) ∴ b−12=a+42 ⇒ a – b = –5 …… (1) Since AB is ⊥ to the line y = x, ∴ product of slope of AB and slope of the line y = x is equal to –1 ⇒b+1a−4×1=−1⇒b+1=−a+4 ⇒ a + b = 3 …… (2) Solving (1) and (2), we get a = –1, b = 4. ∴ Coordinates of the point A are (–1, 4) ∴AB=√(−1−4)2+(4+1)2=5√2

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