Reflections Across the x- or y- Axis Practice

Question

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Question
Square ABCD has vertices A(2,4), B(2,11), C(7,11), and D(7,4). The square ABCD is reflected on the x-axis and the y-axis. Find the coordinates of the vertices for square A′B′C′D′. Choose 1 for Option A and 2 for Option B.

Option A: Square A′B′C′D′ has vertices A′(−2,−4), B′(−2,−11), C′(−7,−11), and D′(−7,−4).
Option B: Square A′B′C′D′ has vertices A′(2,−4), B′(2,−11), C′(7,−11), and D′(7,−4).(1 point)

Answer 1

The correct answer is Option A: Square A′B′C′D′ has vertices A′(−2,−4), B′(−2,−11), C′(−7,−11), and D′(−7,−4).

When a shape is reflected across the x-axis, the y-coordinates of the vertices are changed to their opposites, while the x-coordinates remain the same. When a shape is reflected across the y-axis, the x-coordinates of the vertices are changed to their opposites, while the y-coordinates remain the same.

In this case, when square ABCD is reflected on the x-axis, the y-coordinates change from positive to negative. Similarly, when square ABCD is reflected on the y-axis, the x-coordinates change from positive to negative.

Using this information, we can find the coordinates for square A′B′C′D′ by changing the signs of the original coordinates of square ABCD.

Square ABCD has vertices A(2,4), B(2,11), C(7,11), and D(7,4).

Reflecting across the x-axis, the y-coordinates change from positive to negative: 4 becomes -4 and 11 becomes -11.

Reflecting across the y-axis, the x-coordinates change from positive to negative: 2 becomes -2 and 7 becomes -7.

Therefore, square A′B′C′D′ has vertices A′(−2,−4), B′(−2,−11), C′(−7,−11), and D′(−7,−4).