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Question
Find the image of the point (−2, 3) about the line x + 2y − 9 = 0
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Solution
The image of the point (x1, y1) about the line ax + by + c = 0 is
`(x - x_1)/"a" = (y - "y"_1)/"b" = +- (2("a"x_1 + "b"y_1 + "c"))/("a"^2 + "b"^2)`
∴ The image of the point (– 2, 3) about the line x + 2y – 9 = 0 is
`(x + 2)/1 = (y - 3)/2 = +- (2[(- 2) + 2(3) - 9])/(1^2 + 2^2)`
`(x + 2)/1 = (y - 3)/2 = +- (2(- 2 + 6 - 9))/(1 + 4)`
`(x + 2)/1 = (y - 3)/2 = +- (- 10/5)`
x + 2 = – 2, `(y - 3)/2` = 2
x = 2 – 2, y – 3 = 4
x = 0, y = 4 + 3 = 7
∴ The required point is (0, 7)
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