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Summer Work: Parallel Layout Checks

Students experiment with rotations, reflections, and translations to check parallel lines in mowing and babysitting layouts.

Grade 8MathInteractive · Printable

Aligned to8.G.A.1.c

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
13 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Sorting, Short answer

About this worksheet

What students practice

Students test whether rotations, reflections, and translations preserve parallel lines.
Students use image coordinates and line directions as evidence of parallelism.
Students distinguish valid experimental evidence from incomplete checks of parallel lines.

How to use

Provide graph paper, tracing paper, and a straightedge. Have students perform each motion, draw the image lines, and use their results to answer the questions.

Curriculum

Common Core standard covered

8.G.A.1.c

Check by experiment that rotations, reflections, and translations move parallel lines to parallel lines.

Preview

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Name Date

Summer Work: Parallel Layout Checks

Test how rigid motions affect parallel lines in lawn and babysitting layouts.

Rotate a Mowing Layout

Lena and Omar mow lawns and babysit during summer break. Their layout sketches use full lines, not just short segments. Use graph paper, tracing paper, and a straightedge to test each motion.

The lines through A and B and through C and D represent two parallel mowing guides. Copy the points and draw both full lines. Trace the pair, then rotate the tracing 180° about (1, 0). To check a point, its image coordinates are (2 − x, −y).

Complete the turn on your tracing. Which record correctly gives all four image points?

A. A′(−3, −1), B′(1, −3), C′(−3, 2), D′(1, 0)
B. A′(5, −1), B′(1, −3), C′(5, 2), D′(1, 0)
C. A′(5, 1), B′(1, 3), C′(5, −2), D′(1, 0)
D. A′(3, −1), B′(−1, −3), C′(3, 2), D′(−1, 0)

Draw the two image lines through A′B′ and C′D′. At x = 1, the image points have y-coordinates −3 and 0. At x = 5, they have y-coordinates −1 and 2. Measure the vertical gap at both locations.

At x = 1, the vertical gap is units. At x = 5, the vertical gap is units.

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