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Scale drawings and transformations — SHSAT practice questions

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. A student must scale lengths linearly and areas by the square of that factor, then find where a point lands after a 180° rotation about the origin, a reflection across an axis, or both in sequence. Questions are multiple choice, with options that are usually coordinate pairs or an area on the drawing. Traps include treating area like length, mixing the order of the two moves, and reversing coordinate signs.

  • Section: Mathematics 57 questions on the paper
  • 112 practice questions in the app

Sample questions

Question 1

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?

  1. A16 cm2^2
  2. B18 cm2^2
  3. C48 cm2^2
  4. D54 cm2^2
Show answer

Answer: B — 18 cm2^2

Areas scale by the square of the length ratio: 9 cm2^2 stands for 64 m2^2, so 128 m2^2 becomes 2×9=182\times9=18 cm2^2.

Question 2

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

  1. A(a,−b)(a,-b)
  2. B(−a,b)(-a,b)
  3. C(−a,−b)(-a,-b)
  4. D(b,a)(b,a)
Show answer

Answer: A — (a,−b)(a,-b)

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

Question 3

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

  1. A(1,−2)(1,-2)
  2. B(2,−2)(2,-2)
  3. C(1,−3)(1,-3)
  4. D(−1,−1)(-1,-1)
Show answer

Answer: A — (1,−2)(1,-2)

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

Practice 112 Scale drawings and transformations questions in the app

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