Question

The point a is shown below.
Reflect a across the -axis.
Then reflect the result across the -axis.
its 6,0

Answer 1

To reflect the point \( a(6, 0) \) across the x-axis, we change the sign of the y-coordinate. The reflection of \( a(6, 0) \) across the x-axis is:

\[
a'(6, 0) \rightarrow (6, -0) \rightarrow (6, 0)
\]

Since the y-coordinate remains 0, the point does not change.

Now, to reflect this result \( a'(6, 0) \) again across the y-axis, we change the sign of the x-coordinate. The reflection of \( a'(6, 0) \) across the y-axis is:

\[
a''(6, 0) \rightarrow (-6, 0)
\]

So, after reflecting the point \( a(6, 0) \) first across the x-axis and then across the y-axis, the final result is:

\[
\text{Final point: } (-6, 0)
\]