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Hiking Trip: Trail Map Overlays worksheet preview

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Hiking Trip: Trail Map Overlays

Compare hiking trail diagrams using rotations, reflections, translations, and dilations, and justify when the diagrams are similar.

Grade 8MathInteractive · Printable

Aligned to8.G.A.4

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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, Short answer, Drawing

About this worksheet

What students practice

  • Students identify sequences of rigid motions and dilations that map corresponding trail vertices.
  • Students determine whether trail diagrams are similar using lengths, angles, and transformations.
  • Students describe and verify transformations using corresponding coordinates.

How to use

Use after students practice individual transformations. Have students trace intermediate images and check every corresponding vertex before accepting a sequence.

Curriculum

Common Core standard covered

8.G.A.4

Understand similar figures as ones linked by rotations, reflections, translations, and dilations, and describe such a sequence.

Preview

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Name Date

Hiking Trip: Trail Map Overlays

Use transformation sequences to compare trail diagrams.

Map Tools

Each coordinate grid shows a flat map, not an elevation profile. Connected points mark trail segments. All dilation factors are positive.

1.
The trip leader moves this trail diagram to a larger map panel. The corresponding new vertices are P(2, 2), Q(2, 6), and R(4, 2), with A → P, B → Q, and C → R. Which sequence works?−4−3−2−112340−4−3−2−11234ABC
  • A. Rotate 90° counterclockwise about the origin, then dilate by 2 about the origin.
  • B. Rotate 90° clockwise about the origin, then dilate by 2 about the origin.
  • C. Rotate 180° about the origin, then dilate by 2 about the origin.
  • D. Reflect across the y-axis, then dilate by 2 about the origin.
2.
A close-up map is made by dilating this diagram by 2, centered at trailhead T. Find the new location of lookout L.−5−4−3−2−1123450−5−4−3−2−112345TL

The image of L is ( ,  ).

3.
A pocket map places the images of D, E, and F at (2, −1), (1, −1), and (1, −2), respectively. Which sequence maps the displayed trail onto the pocket-map trail?−5−4−3−2−1123450−5−4−3−2−112345DEF
  • A. Rotate 180° about the origin, then dilate by 1/2 about the origin.
  • B. Reflect across the x-axis, then dilate by 1/2 about the origin.
  • C. Reflect across the y-axis, then dilate by 2 about the origin.
  • D. Reflect across the y-axis, then dilate by 1/2 about the origin.

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