In lesson 4, you completed a construction exercise that resulted in a pair of parallel lines (Problem 1 from the Problem Set). Now we examine an alternate construction.

Construct the line parallel to **a** given line **AB **through **a** given point **P**.

1. Draw circle **P**: Center **P**, radius **AB**.

2. Draw circle **B**: Center **B**, radius **AP**.

3. Label the intersection of circle **P** and circle **B** as **Q**.

4. Draw **PQ.**

Note: Circles **P ** and **B** intersect in two locations. Pick the intersection **Q** so that points **A **and **Q** are in opposite half-planes of line **PB**.

Draw your sketch on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Graph is on paper."

Modified from EngageNY ©Great Minds Disclaimer

Draw the vector that defines each translation below

a)

Finding the vector is relatively straightforward. Applying a vector to translate a figure is more challenging. To translate a figure, we must construct parallel lines to the vector through the vertices of the original figure and then find the points on those parallel lines that are the same direction and distance away as given by the vector.

Draw your vector on paper, take a picture, and upload it using the image upload icon

If you do not have the ability to upload an image of your work, type "Vector is on paper."

Modified from EngageNY ©Great Minds Disclaimer

b)

c)

Use your compass and straightedge to apply 𝑇 𝐴𝐵 to segment 𝑃1𝑃2 . Note: Use the steps from the Exploratory Challenge twice for this question, creating two lines parallel to 𝐴𝐵 : one through 𝑃1 and one through 𝑃2 .

Draw your vector on paper, take a picture, and upload it using the image upload icon

If you do not have the ability to upload an image of your work, type "Vector is on paper."

Modified from EngageNY ©Great Minds Disclaimer

Use your compass and straightedge to apply 𝑇 𝐴𝐵 to △ 𝑃1𝑃2𝑃3 .

Draw your vector on paper, take a picture, and upload it using the image upload icon

If you do not have the ability to upload an image of your work, type "Vector is on paper."

Modified from EngageNY ©Great Minds Disclaimer