Question

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

Answer 1

A.

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.

Answer 2

Answer: 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.