Question

A point $P$ is reflected in the $x$-axis. Co-ordinates of its image are $(8,-6)$. Find the co-ordinates of $P$. Find the
co-ordinates of the image of $P$ under reflection in the
$y$-axis.

Answer 1

Step $1$: Find the coordinates of $P$

Given: Co-ordinates of the image of $P$ reflected in the $x$-axis $=(8,-6)$

Reflection in the $x$-axis, $M_x(x,y)=(x,-y)$

$\Rightarrow M_x(x,y)=(8,-6)$

So,

$x=8$

$-y=-6\Rightarrow y=6$

Hence, the co-ordinates of $P$ are $(8,6)$.

Step $2$: Find the co-ordinates of the image of $P$ reflected in the $y$-axis

Co-ordinates of $P=(8,6)$

Reflection in the $y$-axis, $M_y(x,y)=(-x,y)$

$\Rightarrow M_y(8,6)=(-8,6)$

Hence, the co-ordinates of the image of $P$ reflected in the $y$-axis are $(-8,6)$.