Straight Lines
Reflection — Image on Circle
DAILY_CHALLENGE
Grade 11
Question:
If the image of the point $(-4,5)$ in the line $x+2y=2$ lies on the circle $(x+4)^2+(y-3)^2=r^2$, then $r$ is equal to:
Step-by-Step Solution
Key Concept: Image of $(-4,5)$ in $x+2y-2=0$: use formula $\frac{x+4}{1}=\frac{y-5}{2}=-2\cdot\frac{-4+10-2}{1+4}=-\frac{8}{5}$.
Image $=(-28/5,9/5)$. $r^2=4$, $r=2$.
Correct Answer: 1