Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Which of these points is 4 to the left of the vertical axis and 1 up?
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(−4, 1).
2 Reflect the point (5, 1) in the horizontal axis and write the two coordinates of where it lands.
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5, -1 — the point (5, −1).
3 The point (6, 2) is reflected in the vertical axis. What is the first coordinate of the new point?
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-6.
Level 2 · Core
4 Where does (−5, 1) land after a half turn about the origin?
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(5, −1).
5 The point (1, 4) is turned a quarter turn anticlockwise about the origin. Write the two coordinates of where it lands.
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-4, 1 — the point (−4, 1).
6 A point is reflected in the horizontal axis and lands at (3, −7). What was its second coordinate before the reflection?
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7 — it was at (3, 7).
Level 3 · Challenge
7 Think about the point (2, −3).1 It lies below the horizontal axis.
2 Reflected in the vertical axis it becomes (−2, −3).
3 After a half turn about the origin it becomes (2, 3).
Which statements are correct?
2 Reflected in the vertical axis it becomes (−2, −3).
3 After a half turn about the origin it becomes (2, 3).
Which statements are correct?
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The second number is negative, so it is below the axis (1 ✓); the vertical mirror flips the first to give (−2, −3) (2 ✓). A half turn gives (−2, 3), not (2, 3) (3 ✗). 1 and 2.
8 The point (3, 2) is turned a quarter turn anticlockwise about the origin, and then reflected in the horizontal axis. Write the coordinates after each step.
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The quarter turn gives (-2, 3), and reflecting that gives (−2, -3).
9 How many quarter turns about the origin bring a point back to where it started?
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4.