Reflections and rotations
Reflect points and shapes in the x-axis or y-axis, rotate points 90° and 180° about the origin, and identify transformations from original and image coordinates.
Worked examples
Reflecting a point in the x-axis
Straightforward
Problem
Reflect the point in the -axis. State the new coordinates.
1
Write the rule for a reflection in the -axis.
2
Apply the rule to : keep the -coordinate and change the sign of the -coordinate.
Answer
Rotating a point 180° about the origin
Moderate
Problem
Rotate the point by about the origin. State the new coordinates.
1
Write the rule for a rotation about the origin.
2
Apply the rule to : change the sign of both coordinates.
Answer
Identifying a transformation from original and image coordinates
Challenging
Problem
The point maps to . Identify the transformation.
1
Test reflection in the -axis: .
✗
2
Test reflection in the -axis: .
✗
3
Test a anticlockwise rotation: .
✓
4
State the transformation.
The image matches, so the transformation is a rotation of anticlockwise about the origin.
Answer
Rotation of anticlockwise about the origin
Practise
Q1·Straightforward
Reflect the point in the -axis. State the new coordinates.
Explanation
Reflecting in the -axis: . So .
Q2·Straightforward
Reflect the point in the -axis. State the new coordinates.
Explanation
Reflecting in the -axis: . So .
Q3·Straightforward
Reflect the point in the -axis. State the new coordinates.
Explanation
Reflecting in the -axis: . So .
Q4·Straightforward
Reflect the point in the -axis. State the new coordinates.
Explanation
Reflecting in the -axis: . So .
Q5·Moderate
Rotate the point by anticlockwise about the origin. State the new coordinates.
Explanation
A anticlockwise rotation maps . So .
Q6·Moderate
Rotate the point by about the origin. State the new coordinates.
Explanation
A rotation maps . So .
Q7·Moderate
Rotate the point by clockwise about the origin. State the new coordinates.
Explanation
A clockwise rotation maps . So .
Q8·Moderate
Rotate the point by anticlockwise about the origin. State the new coordinates.
Explanation
A anticlockwise rotation maps . So .
Q9·Challenging
The point maps to . Which transformation was applied?
Explanation
The -coordinate changed from to and the -coordinate stayed at . This matches the rule , which is a reflection in the -axis.
Q10·Challenging
The point maps to . Which transformation was applied?
Explanation
A clockwise rotation maps . Applying this to : . This matches , confirming a clockwise rotation about the origin.
Q11·Challenging
The point maps to . Which transformation was applied?
Explanation
A rotation maps . Applying this to : . This matches , confirming a rotation of about the origin.
Q12·Challenging
The point maps to . Which transformation was applied?
Explanation
A anticlockwise rotation maps . Applying this to : . This matches , confirming a rotation of anticlockwise about the origin.
Open Math
Reflections and rotations
Space · MA4-GEO-C-01
Name:
Date:
Q1Straightforward
Reflect the point in the -axis. State the new coordinates.
Q2Straightforward
Reflect the point in the -axis. State the new coordinates.
Q3Straightforward
Reflect the point in the -axis. State the new coordinates.
Q4Straightforward
Reflect the point in the -axis. State the new coordinates.
Q5Moderate
Rotate the point by anticlockwise about the origin. State the new coordinates.
Q6Moderate
Rotate the point by about the origin. State the new coordinates.
Q7Moderate
Rotate the point by clockwise about the origin. State the new coordinates.
Q8Moderate
Rotate the point by anticlockwise about the origin. State the new coordinates.
Q9Challenging
The point maps to . Which transformation was applied?
- A.Reflection in the -axis
- B.Reflection in the -axis
- C.Rotation of anticlockwise about the origin
- D.Rotation of about the origin
Q10Challenging
The point maps to . Which transformation was applied?
- A.Reflection in the -axis
- B.Reflection in the -axis
- C.Rotation of anticlockwise about the origin
- D.Rotation of clockwise about the origin
Q11Challenging
The point maps to . Which transformation was applied?
- A.Reflection in the -axis
- B.Reflection in the -axis
- C.Rotation of clockwise about the origin
- D.Rotation of about the origin
Q12Challenging
The point maps to . Which transformation was applied?
- A.Reflection in the -axis
- B.Reflection in the -axis
- C.Rotation of anticlockwise about the origin
- D.Rotation of clockwise about the origin
Worked solutions and answers at openmath.au/year-8/properties-of-geometrical-figures/reflections-and-rotations