Question

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

• A. (4, 8)
• B. (6, 5)
• C. (6, 8)
• D. (0, 10)

Answer 1

Answer: (C)

Let $Q(\alpha ,\beta )$ 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 meet with $x+y-10=0$ at $(4,6),$ then $\frac{\alpha +2}{2}=4,\frac{\beta +4}{2}=6\Rightarrow \alpha =6,\beta =8$