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Grade 8 Transformation Geometry Quiz

Translations, Reflections, Rotations and Enlargements

What this quiz covers

grade8_transformation_geometry_quiz1 draws its questions at random from a bank of 13 questions, with full worked solutions for every one.

Worked examples

A few of the question types, with full solutions, so you know what to expect.

Which transformation is NOT rigid (does not keep the shape congruent)?

  1. Enlargement
  2. Translation
  3. Reflection
  4. Rotation

Answer: Enlargement

\(\text{Translations, reflections and rotations keep size and shape.}\)

\(\text{An enlargement changes the size, so the image is similar, not congruent.}\)

The point \(P(2;\ 3)\) is translated 3 right and 2 down. What is \(P'\)?

  1. \((5;\ 1)\)
  2. \((5;\ 5)\)
  3. \((-1;\ 1)\)
  4. \((1;\ 5)\)

Answer: \((5;\ 1)\)

\(x: 2+3=5\)

\(y: 3-2=1\)

Point \(A(1;\ 4)\) maps to \(A'(-2;\ 6)\). What is the translation rule?

  1. \((x-3;\ y+2)\)
  2. \((x+3;\ y-2)\)
  3. \((x-1;\ y+2)\)
  4. \((x-3;\ y-2)\)

Answer: \((x-3;\ y+2)\)

\(\text{Subtract: image minus object.}\)

\(x: -2-1=-3 \text{ (3 left)}\)

\(y: 6-4=+2 \text{ (2 up)}\)

Reflect \(A(3;\ 2)\) in the x-axis. What is \(A'\)?

  1. \((3;\ -2)\)
  2. \((-3;\ 2)\)
  3. \((-3;\ -2)\)
  4. \((2;\ 3)\)

Answer: \((3;\ -2)\)

\(\text{x-axis reflection: } (x;\ y) \rightarrow (x;\ -y)\)

\(x \text{ stays, } y \text{ changes sign.}\)

Reflect \(B(-5;\ 1)\) in the y-axis. What is \(B'\)?

  1. \((5;\ 1)\)
  2. \((-5;\ -1)\)
  3. \((5;\ -1)\)
  4. \((1;\ -5)\)

Answer: \((5;\ 1)\)

\(\text{y-axis reflection: } (x;\ y) \rightarrow (-x;\ y)\)

\(y \text{ stays, } x \text{ changes sign.}\)