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Question

The image of the point (–8, 12) with respect to the line mirror 4x + 7y + 13 = 0 is


A

(16, –2)

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B

(–16, 2)

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C

(16, 2)

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D

(–16, –2)

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Solution

The correct option is D

(–16, –2)


Equation of the given line is

4x + 7y + 13 = 0 …… (1)

Let Q(α, β) be the image of the point P(–8, 12) with respect to line (1)

Then, PQ line (1) and PC = CQ

Equation of the line PC is

(y12)=74(x+8)

[PC is to the line (1) and passes through (–8, 12)]

or 7x – 4y + 104 = 0 …… (2)

solving (1) and (2), we get

x = –12 and y = 5.

C(12,5)

Since C is mid point of PQ,

12=α82 and 5=β+122

α=16 and β=2 Q(16,2)


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