Use the image to answer the question. Reflect square ABCD first across the x -axis, and then across the y -axis to create square A′B′C′D′ . What are the vertices of square A′B′C′D′ ? (1 point)

Question

Square A′B′C′D′ has vertices A′(−3,−4) , B′(−7,−4) , C′(−7,−8) , and D′(−3,−8)
Square A′B′C′D′ has vertices A′(3,4) , B′(7,4) , C′(7,8) , and D′(3,8)
Square A′B′C′D′ has vertices A′(−3,4) , B′(−7,4) , C′(−7,8) , and D′(−3,8)
Square A′B′C′D′ has vertices A′(−3,4) , B′(−7,4) , and C′(−7,8)

Answer 1

To find the vertices of square A′B′C′D′ after reflecting square ABCD first across the x-axis and then across the y-axis, we follow these steps:

1. Identify the original vertices of square ABCD. Let's assume that the vertices are:

   • A(x1, y1)
   • B(x2, y2)
   • C(x3, y3)
   • D(x4, y4)

2. Reflect across the x-axis. The reflection rule across the x-axis is to change the sign of the y-coordinate:

   • A’(x1, -y1)
   • B’(x2, -y2)
   • C’(x3, -y3)
   • D’(x4, -y4)

3. Reflect across the y-axis. The reflection rule across the y-axis is to change the sign of the x-coordinate:

   • A’’(-x1, -y1)
   • B’’(-x2, -y2)
   • C’’(-x3, -y3)
   • D’’(-x4, -y4)

Now substituting the coordinates from square ABCD into the above steps (assuming for example, A(3, 4), B(7, 4), C(7, 8), D(3, 8) as original vertices):

1. Reflect across the x-axis:

   • A’(3, -4)
   • B’(7, -4)
   • C’(7, -8)
   • D’(3, -8)

2. Reflect across the y-axis:

   • A’’(-3, -4)
   • B’’(-7, -4)
   • C’’(-7, -8)
   • D’’(-3, -8)

This gives us the vertices of square A′B′C′D′:

• A′(-3, -4)
• B′(-7, -4)
• C′(-7, -8)
• D′(-3, -8)

Therefore, the correct answer is: Square A′B′C′D′ has vertices A′(−3,−4) , B′(−7,−4) , C′(−7,−8) , and D′(−3,−8).