Question

What is point
𝐴
A
(
−
6
,

−
6
)
(−6, −6) after a translation of
2
2 units right and
1
1 units up followed by a reflection over the x-axis.

Answer 1

To find the new position of point \( A(-6, -6) \) after the specified transformations, we can break it down into two steps: the translation and the reflection.

1. **Translation**:
- Moving 2 units to the right means we add 2 to the x-coordinate.
- Moving 1 unit up means we add 1 to the y-coordinate.

Starting with point \( A(-6, -6) \):
\[
x' = -6 + 2 = -4
\]
\[
y' = -6 + 1 = -5
\]
After the translation, point \( A \) moves to \( A'(-4, -5) \).

2. **Reflection over the x-axis**:
- When reflecting a point over the x-axis, the x-coordinate remains the same, while the y-coordinate changes sign.

Starting with point \( A'(-4, -5) \):
\[
x'' = -4
\]
\[
y'' = -(-5) = 5
\]
After the reflection, point \( A \) moves to \( A''(-4, 5) \).

Thus, after the translation and reflection, the final position of point \( A \) is:
\[
\boxed{(-4, 5)}
\]