Which of the following sequences of transformations maps
figure 1 to figure 2?
90° clockwise rotation around
the origin, then a reflection
across the x-axis
90° counterclockwise rotation
around the origin, then a
reflection across the x-axis
-4
reflection across the y-axis, then
a reflection across the x-axis
reflection across the x-axis, then
a reflection across the y-axis

Explanation:

The vertices of the figure 1 are:

The vertices of figure 2 are:

By simple inspection, you can tell that if you rotate the figure 1 90º clockwise and then reflect the image across the x-axys you obtain the figure 2.

You can prove that analitically.

1. Rotation 90º clockwise

A 90º clockwise reotation is the same that a 270º counterclockwise rotation and the mathematical rule for this is:

Applying that rule to the vertices of figure 1, you obtain:

2. Reflection across the x-axis.

A reflection across the x-axis keeps the same x-coordinate and changes the sign of the y-coordinate. The rule is:

Applying that rule to the previous points yields to:

Which are the coordinates of the figure 2. Thus, you have proved that the sequence of transformations 90° clockwise rotation around the origin, then a reflection across the x-axis (first choice) maps the figure 1 to figure 2.

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step-by-step explanation: