Question

02.02 MC) 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 negative 4, negative 2, B double prime at negative 4, negative 1, C double prime at negative 1, negative 1, D double prime at negative 1, negative 2. 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

To transform rectangle ABCD to A″B″C″D″, the given set of transformations is a reflection over the y-axis and rotation of 180°.

What is transformation?

Given that

A(-4,2), B(-4,1), C(-1,1) and D(-1,2)

A"(-4,-2) B"(-4,-1), C"(-1,-1) and D"(-1,-2)

Reflection over the y-axis:

Negate the x-coordinates, flipping the shape horizontally

A(-4,2), B(-4,1), C(-1,1) and D(-1,2)

Multiple the x coordinates by -1

A'(4,2), B'(4,1), C'(1,1) and D'(1,2)

.180° Rotation:

Negate both x and y-coordinates, effectively rotating the shape half-way around the origin.

A'(4,2), B'(4,1), C'(1,1) and D'(1,2)

multiple both x and y coordinates with -1

A"(-4,-1), B"(-4,-1) , C"(-1,-1) and D"(-1,-2).

Therefore,the transformations are Reflection over the y-axis and rotation of 180°.