Question

solve each of the problems below. be sure to ask questions if you need more help with a topic.i can generalize the properties of orientation and congruence of transformations.1. reflect the figure over the x-axis. then, mark the statements as true or false.____ a. the corresponding sides in the pre-image and image are congruent.__ b. the reflection changed the orientation of the vertices.2. translate the figure 8 units left and 2 units up. then, mark the statements as true or false.__ a. the pre-image is located in quadrant iii.__ b. the pre-image and image are congruent figures.3. rotate the figure 90° clockwise. then, mark the statements as true or false.__ a. the orientation of the figure did not change.__ b. the corresponding angle measures in the pre-image and image are congruent.4. dilate the figure by a scale factor of 2.5. then, mark the statements as true or false.__ a. the orientation of the figure did not change.____ b. the ratios of corresponding sides are all equal to 2.5.@maneuvering the middle llc, 2016

Explanation:

Step1: Analyze Problem 1 (Reflection)

Step1a: Check congruence after reflection

Reflection is a rigid transformation, so pre-image and image sides are congruent.

Step1b: Check orientation change

Reflection flips the figure, reversing vertex orientation.

Step2: Analyze Problem 2 (Translation)

Step2a: Identify pre-image quadrant

Pre-image has positive x, negative y: Quadrant IV, not III.

Step2b: Check congruence after translation

Translation is rigid, so pre-image and image are congruent.

Step3: Analyze Problem 3 (90° Clockwise Rotation)

Step3a: Check orientation change

Rotation rearranges vertex order, changing orientation.

Step3b: Check angle congruence after rotation

Rotation is rigid, so corresponding angles are congruent.

Step4: Analyze Problem 4 (Dilation)

Step4a: Check orientation change

Dilation only scales, so orientation stays the same.

Step4b: Check side ratio with scale factor

Dilation by scale factor $k$ gives side ratio $k=2.5$.

Answer:

1.
a. True
b. True
2.
a. False
b. True
3.
a. False
b. True
4.
a. True
b. True