The image of the point (2, 4) in the line x + y - 10 = 0 is

Question

The image of the point (2, 4) in the line $x + y - 10 = 0$ is

Smart Achievers · Accepted Answer

(3)

$Let Q (α, β) be the image of point P (2, 4) in the line x + y - 10 = 0$

$The equation of line passing through$ $P (2, 4)$ $and perpendicular to$ $x + y - 10 = 0$ $is$ $(y - 4) = 1 (x - 2)$ $i.e.,$ $- x + y - 2 = 0$

$This meets with$ $x + y - 10 = 0$ $at$ $(4, 6)$ ,

$Then,$ $\frac{α + 2}{2} = 4, \frac{β + 4}{2} = 6$ $\Rightarrow$ $α = 6, β = 8$

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