What set of reflections and rotations would carry rectangle abcd onto itself? rectangle formed by ordered pairs a at negative 4, 1, b at negative 4, 2, c at negative 1, 2, d at negative 1, 1. (4 points)
reflect over the y-axis, reflect over the x-axis, rotate 180°
rotate 180°, reflect over the x-axis, reflect over the line y=x
reflect over the x-axis, rotate 180°, reflect over the x-axis
rotate 180°, reflect over the y-axis, reflect over the line y=x

A.

Step-by-step explanation:

Reflect in the y-axis.

this takes it to the first quadrant.

Reflect in the  x-axis.

To the fourth quadrant

Rotate through through 180 degrees.

Back to its original location.

 The correct option is

(A) Reflect over the y-axis, reflect over the x-axis, rotate 180°.

Step-by-step explanation:  Given that the co-ordinates of the vertices of rectangle ABCD are A(-4, 1), B(-4, 2), C(-1, 2) and D(-1, 1).

We are to select the set of reflections and rotations that would carry rectangle ABCD onto itself.

We see that if a point (x, y) is first reflected across Y-axis, its co-ordinates becomes

(x, y)   ⇒    (-x, y).

Now, if the new point is reflected across X-axis, then its co-ordinates becomes

(-x, y)  ⇒  (-x, -y)

and finally if we rotate the point by 180 degrees, its co-ordinates becomes

(-x, -y)  ⇒  (x, y).

That is, after these three transformations, each of the vertex of rectangle ABCD, that is, A(-4, 1), B(-4, 2), C(-1, 2) and D(-1, 1) come back to its original position.

Thus, the required set of reflections and rotations would carry rectangle ABCD onto itself is

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

Option (A) is CORRECT.

the answer will be

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step-by-step explanation: