What set of Reflections and rotations could carry ABCD onto itself?

Reflect over y-axis,reflect over the X axis ,rotate 180°

Option D is the correct option.

Explanation:

Let's take point A which is (4,-1)

Reflection over y- axis will make this point (4,1)

Then, reflection over X axis will make this point (4,-1)

After rotation of 180 degree we will get (-4,1) .

Please see the attached picture....

Hope it helps...

Good luck on your assignment...

 d) reflect over the x-axis, reflect over y-axis, rotate 180°

Step-by-step explanation:

A reflection over the x-axis and a reflection over the y-axis is the SAME as a rotation of 180°. Together they make a rotation of 360°, which results in the image staying at the same place.

Reflection over the x-axis changes the sign of the y-coordinate

Z = (x, y)    →    Z' = (x, -y)

Reflection over the y-axis changes the sign of the x-coordinate

Z' = (x, -y)    →    Z'' = (-x, -y)

Rotation of 180° changes the signs of both the x- and y-coordinates

Z'' = (-x, -y)   →     Z''' = (x, y)

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step-by-step explanation: