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) .
To reflect a point on the x-axis, we simply change the sign of the y-coordinate. To reflect a point on the y-axis, we change the sign of the x-coordinate.
For the x-axis reflection, the y-coordinates of the vertices will become negative. Therefore, the coordinates of square A′B′C′D′ will be A′(2,-4), B′(2,-11), C′(7,-11), and D′(7,-4).
For the y-axis reflection, the x-coordinates of the vertices will become negative. Therefore, the coordinates of square A′B′C′D′ will be A′(-2,4), B′(-2,11), C′(-7,11), and D′(-7,4).
Comparing the coordinates with the given options, we can see that Option B is the correct answer. So the coordinates of square A′B′C′D′ are A′(2,−4), B′(2,−11), C′(7,−11), and D′(7,−4).