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)
wrong, its option A
The reflection of a point (x, y) on the x-axis is (-x, y), and the reflection of a point on the y-axis is (x, -y).
For the given square ABCD, the x-coordinates of A and B are the same, and the y-coordinates of B and C are the same.
Thus, when reflecting the square on the x-axis, the x-coordinates of the vertices remain the same, but the y-coordinates change sign.
Similarly, when reflecting the square on the y-axis, the y-coordinates of the vertices remain the same, but the x-coordinates change sign.
Using these reflection properties, we can determine the coordinates of the vertices for square A′B′C′D′.
For vertex A, the reflection on the x-axis gives (-2, 4).
For vertex B, the reflection on the x-axis gives (-2, 11).
For vertex C, the reflection on the x-axis gives (-7, 11).
For vertex D, the reflection on the x-axis gives (-7, 4).
Reflecting this result on the y-axis, we get A′(2,−4), B′(2,−11), C′(7,−11), and D′(7,−4).
Therefore, the coordinates of the vertices for square A′B′C′D′ are 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)
To find the coordinates of the vertices for square A′B′C′D′ after reflection on the x-axis and y-axis, we need to flip the sign of the y-coordinates and x-coordinates, respectively.
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).
The correct answer is Option B.