Question

lesson 3: translating lines exercises all lines provided are labeled \l\. 1. draw a line passing through point p that is parallel to line l. draw a second line passing through point p that is parallel to line l and that is distinct (i.e., different) from the first one. what do you notice? 2. translate line l along the vector ab. what do you notice about l and its image, l? eureka math lesson 3: translating lines

Explanation:

Step1: Recall parallel - line property

Parallel lines have the same slope. When drawing a line through point $P$ parallel to line $L$, we use a straight - edge to ensure the new line has the same direction as $L$.

Step2: Analyze translation of a line

When we translate line $L$ along the vector $\overrightarrow{AB}$, every point on line $L$ is moved the same distance and in the same direction as the vector $\overrightarrow{AB}$. Since the translation is a rigid motion, the line and its image are identical.

Answer:

1. When drawing a line through point $P$ parallel to line $L$, the new line is parallel to $L$ and has the same slope as $L$.
2. When translating line $L$ along the vector $\overrightarrow{AB}$, the line $L$ and its image $L'$ are the same line, i.e., $L = L'$.