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Grade 9 · unit review

Review: Distances and Scaled Designs

Use right triangles, coordinates, and similarity to reason about fictional designs.

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Unit review questions
1. What is the diagonal of an 8-by-15 rectangular panel?
2. What is the distance from (0,0) to (5,12)?
3. A figure is dilated by factor 3. What happens to a corresponding 10-unit side?
4. A 3-by-6 rectangle is enlarged by length factor 2. What is its area?

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Use the skills in a new task

Prepare a paper design note for a fictional 5-by-12 panel. Find its diagonal. Verify that the same distance separates opposite vertices (−1,2) and (4,14). Enlarge every length by factor 2 and report the new sides, diagonal, perimeter, and area. Explain the different scaling of length and area; no physical build is required.

Work on paper or in your own document. Explain the choices you made.

  • Calculate the original diagonal as 13 units.
  • Use coordinate differences 5 and 12 to independently recover 13.
  • Scale sides to 10 and 24 and diagonal to 26.
  • Find enlarged perimeter 68 units and area 240 square units.
  • Explain length factor 2 and area factor 4.
Compare with a model response

5² + 12² = 169, so the diagonal is 13. The vertices differ by 5 horizontally and 12 vertically, yielding the same distance. Doubling gives a 10-by-24 panel with diagonal 26 and perimeter 2(10 + 24) = 68. Area is 10 × 24 = 240, four times the original 60.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.