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

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

COMEDKCOMEDK 2012Straight Lines

Solution:

Let $Q(\alpha, \beta)$ be the image of point $P(2, 4)$ in the line $x + y - 10 = 0$
image
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 meet with $x + y- 10 = 0$ at $(4, 6), $ then $\frac{\alpha+2}{2}=4, \frac{\beta+4}{2} =6 \Rightarrow \alpha =6, \beta=8$