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.