Question

What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at 2, negative 4, B double prime 1, negative 4, C double prime at 1, negative 1, D double prime at 2, negative 1. Reflected over the x‒axis and rotated 180° Reflected over the y-axis and rotated 180° Reflected over the x‒axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise

Answer 1

The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°

What is reflection?

"It is a geometric transformation where all the points of an object are reflected on the line of reflection."

For the given question,

The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)

The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at   (-4, -1), C" at (-1, -1) and D" at (-1, -2)

We can observe that the coordinates of ABCD are of the form (-x, y)  where x, and y, are positive numbers

The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)

The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)

And after rotation of 180°, the coordinates would be (-x -y).

Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.

Learn more about geometric transformations here:

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