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Mathematics

Scale drawings and transformations — SHSAT practice questions

  • 115 practice questions in the app
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Practice 115 Scale drawings and transformations questions in the app

What this topic is

A scale such as one inch to four feet applies to lengths, and that is where this topic hides its best-known mistake: areas scale by the square of the factor.

If a drawing's lengths are one-tenth of the real ones, its areas are one-hundredth. Transformations move figures on the coordinate plane. Rotating a figure half a turn about the origin changes the signs of both coordinates, a reflection across the y-axis changes only the sign of x, and a translation shifts every point the same distance.

Scale drawings and transformations questions may combine two moves in a row, so each step should be applied in order.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Harder

A garden is shown on a drawing with a scale of 3 cm to 8 m. The real garden covers 128 square meters. What area does it occupy on the drawing?

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Answer: B — 18 cm2

Areas scale by the square of the length ratio: 9 cm2 stands for 64 m2, so 128 m2 becomes 2×9=18 cm2.

Question 2Mid

A figure is rotated 180∘ about the origin and then reflected across the y-axis. Where does the point (a,b) end up?

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Answer: A — (a,−b)

The rotation gives (−a,−b), and reflecting across the y-axis negates the first coordinate again, giving (a,−b).

Question 3Easier

Point R(−1,2) is rotated 180 degrees about the origin. Where is the image of R?

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Answer: A — (1,−2)

Apply the coordinate rule for the stated move to obtain (1,−2).

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 115 Scale drawings and transformations questions in the app

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