Question : What is the reflection of the point $(4,7)$ over the line $y=–1$?
Option 1: $(–6,7)$
Option 2: $(–4,–9)$
Option 3: $(4,–9)$
Option 4: $(–6,–7)$
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Correct Answer: $(4,–9)$
Solution :
Given: The point is $(4,7)$ and the line is $y=–1$.
The formula for the reflection of the point $(x_1, y_1)$ over the line $ax+by+c=0$ is $\frac{x–x_1}{a}=\frac{y–y_1}{b}=\frac{–2(ax_1+by_1+c)}{a^2+b^2}$.
Here, are the values of $a=0$, $b=1$, and $c=1$.
$(x–4)=0$ and $(y–7)=\frac{–2(7+1)}{1}$
⇒ $x=4$ and $y=–16+7$
⇒ $x=4$ and $y=–9$
Hence, the correct answer is $(4,–9)$.
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