Question

If $A=(5,3),$ find $A^{\prime },A^{\prime \prime },$ and $A^{\prime \prime \prime }$ where:
$A^{\prime }$is the reflecting point of $A$ across the $x-$ axis.
$A^{\prime \prime }$ is the reflecting point of $A^{\prime }$ across the $y-$ axis.
$A^{\prime \prime \prime }$ is the reflecting point of $A^{\prime \prime }$ across the $x-$ axis.

• A. $A^{\prime }=(5,-3);A^{\prime \prime }=(-5,3);A^{\prime \prime \prime }=(5,3)$
• B. $A^{\prime }=(-5,-3);A^{\prime \prime }=(5,3);A^{\prime \prime \prime }=(5,-3)$
• C. $A^{\prime }=(5,-3);A^{\prime \prime }=(-5,-3);A^{\prime \prime \prime }=(-5,3)$
• D. $A^{\prime }=(-4,-5);A^{\prime \prime }=(5,3);A^{\prime \prime \prime }=(-5,3)$

Answer 1

The correct option is C $A^{\prime }=(5,-3);A^{\prime \prime }=(-5,-3);A^{\prime \prime \prime }=(-5,3)$



Let us first plot the points on the graph and find their reflections.
Coordinates of Point $A:(5,3)$
Distance of Point $A^{\prime }$ from the $y-$ axis toward the right $=5$
Distance of $A^{\prime }$ from the $x-$ axis in the downward direction $=3$
The coordinates of the reflecting Point $A^{\prime }$ across the $x-$ axis $=A^{\prime }(5,-3)$

Coordinates of Point $A^{\prime }:(5,-3)$
Distance of Point $A^{\prime \prime }$ from the $y-$ axis toward the left $=5$
Distance of $A^{\prime \prime }$ from the $x-$ axis in the downward direction $=3$
The coordinates of the reflecting Point $A^{\prime \prime }$ across the $x-$ axis $=A^{\prime \prime }(-5,-3)$

Coordinates of Point $A^{\prime \prime }:(-5,-3)$
Distance of point $A^{\prime \prime \prime }$ from the $y-$ axis towards the left $=5$
Distance of $A^{\prime \prime \prime }$ from the $x-$ axis in the upward direction $=3$
The coordinates of the reflecting Point $A^{\prime \prime \prime }$ across the $x-$ axis $=A^{\prime \prime \prime }(-5,3)$

Hence, option D is correct.