Question

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Answer 1

Answer:

1) Reflection in the x-axis

A' = (-2, -3)

2) Rotation of 180° clockwise about the origin

A'' = (2, 3)

3) Translation of 3 units down and 4 units to the right

A''' = (6, 0)

Step-by-step explanation:

The transformations are as follows;

1) Reflection in the x-axis

Here the x-coordinate is the same and the y-coordinate changes sign.

Therefore, we have;

A (-2, 3)

After reflection in the x-axis becomes A' = (-2, -3)

2) Rotation of 180° clockwise about the origin

When, a point (x, y) is rotated 180° clockwise about the origin, it becomes (-x, -y)

Therefore, we have;

A' = (-2, -3) becomes A'' = (2, 3)

3) Translation of 3 units down and 4 units to the right

Translation of 3 units down and 4 units to the right = $T_{(4, -3)$

Which gives

A''' = (2 + 4, 3 - 3) = (6, 0).