Stage 8 - Q1 - 3 marks
Reflect P in \(y=x\).
Hint
Swap the two coordinates.
Stage 8 - Q2 - 3 marks
Reflect P in \(y=-x\).
Hint
Swap the coordinates and negate both.
Stage 8 - Q3 - 4 marks
Reflect triangle ABC in \(y=x\).
Hint
Swap x and y for each vertex.
Stage 8 - Q4 - 2 marks
Which of \((3,3)\), \((3,-3)\) and \((0,0)\) remain fixed under reflection in \(y=x\)?
Hint
Points on the mirror line are invariant.
Stage 8 - Q5 - 4 marks
Reflect \((2,7)\) in \(y=x\), then in \(y=-x\). Find the final image and name one equivalent transformation.
Hint
Compare the final coordinate rule with a half turn.
Stage 8 - Q6 - 4 marks
A point on \(y=-x\) is reflected in that line. A pupil swaps and negates its coordinates and gets the original point. Is that a mistake? Explain with a nonzero example.
Hint
Choose a point whose coordinates are opposites.
Stage 8 - Q7 - 4 marks
Reflect \((3,5)\) in \(y=x\), then in the x-axis. Find the final image and identify the equivalent rotation about the origin.
Hint
Track the ordered pair through both rules.
Stage 8 - Q8 - 4 marks
Reflection in \(y=x\) maps \((a,5)\) to \((5,2a-3)\). Find a and both points.
Hint
Compare corresponding positions after swapping.
Stage 8 - Q9 - 5 marks
The points on \(y=2x\) are reflected in \(y=x\). Find an equation of the image line and justify using a general point.
Hint
Use a variable point rather than checking only one example.
Stage 8 - Q10 - 6 marks
Reflect a general point in \(y=x\), then in \(x=2\). Show that the result is a 90-degree anticlockwise rotation about \((2,2)\). Verify with P\((1,3)\).
Hint
Compare the combined rule with a rotation of the displacement from (2,2).