Question

The points $P(4,1)$ and $Q(-2,4)$ are reflected in line $y=3$. Find the co-ordinates of $P^{\prime }$, the image of $P$ and $Q^{\prime }$, the image of $Q$.

Answer 1

Consider the diagram shown below which shows the points $P$ and $Q$ and $y=3$ in the same plane.

Now, consider point $P(4,1)$. It is at $3$ units distance from $y=3$. Since, it is reflected by $y=3$, the $x$ coordinate of $P^{\prime }$ will be same as $P$. Also, its $y$ coordinate will be at $3$ units distance to $y=3$ in the opposite side. Therefore, the $y$ coordinate of $P^{\prime }$ will be $5$.

Now, consider point $Q(-2,4)$. It is at $1$ units distance from $y=3$. Since, it is reflected by $y=3$, the $x$ coordinate of $Q^{\prime }$ will be same as $Q$. Also, its $y$ coordinate will be at $1$ units distance to $y=3$ in the opposite side. Therefore, the $y$ coordinate of $Q^{\prime }$ will be $2$.

Therefore,

$\Rightarrow P^{\prime }=(4,5)$

$\Rightarrow Q^{\prime }=(-2,2)$