Question

plane geometry hw: lesson 1 - 18 due fri 9/19 name: zamarri williams pg 1 not accepted after the unit 1 test #3 lesson 1 - 18 hw complete all problems below. show all work. note: images are not drawn to scale. 1.) write a detailed sequence of transformations that takes abcd onto abcd. use your sentence frames to help you. translate abcd so that a lands on a. rotate abcd is congruent to abcd. 2.) write a detailed sequence of transformations that takes δabc onto δabc. use your sentence frames to help you. δabc≅δabc. 3.) in the diagram at right, point k is the center of the circle and the star. a.) rotate the star around point k so that point a lands on point c. hint: use tracing paper to rotate. where does point b land? ______ b.) reflect the star across line ak. hint: you may want to draw the line. where does point b land? ______

Explanation:

Step1: Analyze transformation for ABCD

First, translate polygon ABCD so that point A coincides with point A'. Then, rotate the translated polygon about point A' until it aligns with A'B'C'D'.

Step2: Analyze transformation for ΔABC

Translate triangle ABC so that point A lands on point A'. Then, rotate the translated triangle about point A' to make it coincide with ΔA'B'C'.

Step3: Solve 3a

The star has 5 - fold rotational symmetry. To rotate the star around point K so that A lands on C, we rotate by $\frac{2}{5}\times360^{\circ}=144^{\circ}$ counter - clockwise. Point B will land on point D.

Step4: Solve 3b

When reflecting the star across line AK, point B will land on point E.

Answer:

1. Translate ABCD so that A lands on A'. Then rotate about A' to align with A'B'C'D'.
2. Translate ΔABC so that A lands on A'. Then rotate about A' to align with ΔA'B'C'.
3. a. Point D

b. Point E