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Scale drawings and transformations — SHSAT practice questions

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Practice 112 Scale drawings and transformations questions in the app

What this topic is

Scale drawings and transformations on the SHSAT Mathematics section cover converting a diagram to real lengths or areas with a given scale and moving points on the coordinate plane by rotation and reflection.

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?

A16 cm$^2$✗ Not this oneB18 cm$^2$✓ CorrectC48 cm$^2$✗ Not this oneD54 cm$^2$✗ Not this one

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Answer: B — 18 cm$^2$

Areas scale by the square of the length ratio: 9 cm$^2$ stands for 64 m$^2$, so 128 m$^2$ becomes $2\times9=18$ cm$^2$.

Question 2Mid

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

A$(a,-b)$✓ CorrectB$(-a,b)$✗ Not this oneC$(-a,-b)$✗ Not this oneD$(b,a)$✗ Not this one

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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 $R$?

A$(1,-2)$✓ CorrectB$(2,-2)$✗ Not this oneC$(1,-3)$✗ Not this oneD$(-1,-1)$✗ Not this one

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Answer: A — $(1,-2)$

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

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