Question

What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?

A: Reflected over the x-axis and reflected over the y-axis
B: Reflected over the y-axis and rotated 180°
C: Reflected over the x-axis and rotated 90° counterclockwise
D: Reflected over the y-axis and rotated 90° counterclockwise

Answer 1

The answer is B. when you reflect it, then flip it (rotate 180 deg.) it transforms into that. Let me know if I'm wrong

Answer 2

Answer: A: Reflected over the x-axis and reflected over the y-axis.

Step-by-step explanation:

The rule of reflection across x axis :-

$(x,y)\to\ (x,-y)$

The rule of reflection across y axis :-

$(x,y)\to\ (-x,y)$

From the given figure , the vertices of rectangle ABCD are A(-4,2), B(-4,1), C(-1,1) and D(-1,2)

After reflection across x-axis , the vertices of new rectangle [Let A"B"C"D"] becomes :-

$A(-4,2)\to A"(-4,-2)$

$B(-4,1)\to B"(-4-1)$

$C(-1,1) \to C"(-1,-1)$

$D(-1,2)\to D"(-1,-2)$

Again after reflection across y-axis , the vertices of rectangle A'B'C'D' becomes :-

$A"(-4,-2)\to A'(4,-2)$

$B"(-4-1)\to B'(4,-1)$

$C"(-1,-1)\to C'(1,-1)$

$D"(-1,-2)\to D'(1,-2)$

Hence, the correct  set of transformations could be applied to rectangle ABCD to create A'B'C'D'.