Task Sets: Parallel lines are taken to parallel lines - Common Core Math - Grade 8

Recall / Warm-Up

Two lines are parallel. Which statement about their slopes must be true?

Their slopes are equal (or both lines are vertical)

Their slopes are opposite in sign

Their slopes multiply to give -1

One slope is always 0

A translation by the vector $(3, 2)$ moves the point $(1, 4)$ . What is the new $x$ -coordinate of the image point?

Rigid motions (translations, reflections, rotations) always preserve which of these properties?

Distances and angle measures

Only the position of the origin

Only horizontal directions

Color and size labels

Fluency Practice

$Two parallel lines and their translated images, all four lines at the same steepness$

The parallel lines $y = 2x + 1$ and $y = 2x - 3$ are translated by the vector $(4, 1)$ . What is the slope of each image line?

The parallel lines $y = \frac{1}{2}x + 3$ and $y = \frac{1}{2}x - 1$ are translated by the vector $(2, -5)$ . What is the slope of each image line?

The parallel lines $y = 3x + 2$ and $y = 3x - 4$ are reflected over the y-axis. What are the slopes of the image lines?

Both $-3$ , so the image lines are parallel

Both $3$ , unchanged

One is $3$ and the other is $-3$ , so they are not parallel

Both $\frac{1}{3}$

$Two horizontal lines and their images after a 90-degree counterclockwise turn, shown as two dashed vertical lines$

The horizontal parallel lines $y = 2$ and $y = 5$ are rotated $90\degree$ counterclockwise about the origin. What are the image lines?

The vertical lines $x = -2$ and $x = -5$ , which are parallel

The lines cross, so they are no longer parallel

Still $y = 2$ and $y = 5$ , unchanged

One vertical and one horizontal line

The parallel lines $y = -x + 4$ and $y = -x - 2$ are rotated $90\degree$ counterclockwise about the origin. After the rotation, what is the slope shared by both image lines?

Exercises: Rigid Motions Preserve Parallelism

Recall / Warm-Up

Fluency Practice