Question

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> (i) Point $P(a,b)$ is reflected in the $x$-axis to $P^{\prime }(5,-2)$. Write down the values of a and $b$.
(ii) $P^{\prime \prime }$ is the image of $P$ when reflected in the $y$-axis. Write down the co-ordinates of $P^{\prime \prime }$.
(iii) Name a single transformation that maps $P^{\prime }$ to $P^{\prime \prime }$.

Answer 1

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> (i) As, $M_x(x,y)=(x,-y)$
$P^{\prime }(5,-2)=$ reflection of $P(a,b)$ in $x$-axis.
Hence, the co-ordinates of $P$ are $(5,2)$.
Thus, $a=5$ and $b=2$.
(ii) $P^{\prime \prime }=$ image of $P(5,2)$ reflected in $y$-axis $=(-5,2)$
(iii) Single transformation that maps $P^{\prime }$ to $P^{\prime \prime }$ is the reflection in origin.