Question

lesson 3.2 homework
complete problems 1 - 6 for independent practice.
when you are finished, check the solutions with your teacher.

1. choose the two correct transformations for: rstu to rstu.

a rotation 180°clockwise
b reflection across y = x
c reflection across y = -x
d rotation 180°counterclockwise

1. describe the transformation used for: cdef to cdef.

a reflection across the y - axis
b reflection across y = -1
c reflection across x = -1
d reflection across the x - axis

1. choose the two transformations for: hig to hig.

a rotation 90°clockwise
b reflection across y = x
c reflection across y = -x
d rotation 270°counterclockwise

1. describe the transformation used for: rst to rst.

a reflection across the x - axis.
b reflection across the y - axis
c rotation 180° clockwise
d reflection across y = x

Explanation:

3.

Step1: Analyze rotation and reflection rules

Check the orientation and position of RSTU and R'S'T'U'. A 180 - degree clockwise or counter - clockwise rotation about the origin changes the sign of both x and y coordinates of each point. Also, reflection across \(y=-x\) swaps and negates the x and y coordinates.

Step2: Identify correct transformations

By observing the figure, we can see that the transformation from RSTU to R'S'T'U' can be achieved by either a 180° clockwise rotation or a 180° counter - clockwise rotation.

Step1: Check reflection rules

Examine the position of CDEF and C'D'E'F' with respect to the axes and lines. Reflection across \(y = - 1\) flips the figure over the horizontal line \(y=-1\).

Step2: Determine the transformation

By observing the figure, we can see that the transformation from CDEF to C'D'E'F' is a reflection across \(y=-1\).

Step1: Analyze rotation and reflection rules

Look at the orientation and position of HIG and H'I'G'. A 90 - degree clockwise rotation about the origin changes the coordinates \((x,y)\) to \((y, - x)\). A 270 - degree counter - clockwise rotation also has the same effect.

Step2: Identify correct transformations

By observing the figure, we can see that the transformation from HIG to H'I'G' can be achieved by a 90° clockwise rotation or a 270° counter - clockwise rotation.

Answer:

A. Rotation 180°clockwise
D. Rotation 180°counterclockwise

4.