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 4, negative 2, B double prime at 4, negative 1, C double prime at 1, negative 1, D double prime at 1, negative 2. Reflected over the x‒axis and reflected over the y-axis 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

b- reflect over y- axis and rotate 180 degrees

Explanation:

Reflected about y-axis Rotation of 180°

A= (-4,2) (4,2) A'= (-4,-2)

B= (-4,1) (4,1) B'= (-4,-1)

C= (-1,1) (1,1) C'= (-1,-1)

D= (-1,2) (1,2) D'= (-1,-2)

Answer 2

Reflection over the y-axis and rotation of 180°

Explanation:

We have,

Rectangle ABCD with co-ordinates A(-4,2), B(-4,1), C(-1,1) and D(-1,2).

It is transformed to a new rectangle A'B'C'D' with co-ordinates A'(-4,-2), B'(-4,-1), C'(-1,-1) and D'(-1,-2).

The graph of both the triangles is shown below.

we see that,

The rectangle ABCD is reflected about y-axis and then rotated 180° to obtain A'B'C'D'.

Reflected about y-axis Rotation of 180°

A= (-4,2) (4,2) A'= (-4,-2)

B= (-4,1) (4,1) B'= (-4,-1)

C= (-1,1) (1,1) C'= (-1,-1)

D= (-1,2) (1,2) D'= (-1,-2)

Hence, the second rectangle is formed by: Reflection over the y-axis and rotation of 180°.