Question

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

Answer 1

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

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

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

Hence, option D is correct.