Stage 8 - Q1 - 3 marks
Reflect P in the y-axis.
Hint
Change the x-coordinate sign; keep y.
Stage 8 - Q2 - 3 marks
Reflect P in the line \(y=2\).
Hint
Move three units to the opposite side of the horizontal mirror.
Stage 8 - Q3 - 4 marks
Reflect triangle ABC in \(x=2\).
Hint
Use equal horizontal distances from x=2.
Stage 8 - Q4 - 2 marks
A reflection maps \((2,5)\) to \((8,5)\). Find the mirror line.
Hint
Find the perpendicular bisector between corresponding points.
Stage 8 - Q5 - 3 marks
List all points on the line segment from \((3,-2)\) to \((3,4)\) that stay fixed when reflected in \(x=3\).
Hint
A point on the mirror line is invariant.
Stage 8 - Q6 - 4 marks
Reflect \((4,-3)\) in the x-axis and then the y-axis. Compare with reflecting in the opposite order.
Hint
Track each coordinate through the two steps.
Stage 8 - Q7 - 4 marks
Reflect P\((1,4)\) first in \(x=2\) and then in \(x=5\). Find its final image and one equivalent translation.
Hint
Use the first image as the second reflection’s object.
Stage 8 - Q8 - 4 marks
Reflection in \(y=a\) maps \((3,-2)\) to \((3,10)\). Find a and the image of \((-4,5)\).
Hint
Find the mirror before reflecting the new point.
Stage 8 - Q9 - 5 marks
A point is reflected in \(x=1\), then in \(x=4\), giving final image \((9,-2)\). Find the original point and verify both reflections.
Hint
Undo a sequence in reverse order.
Stage 8 - Q10 - 6 marks
Show that reflecting in \(x=a\) and then \(x=b\) translates every point by \(2(b-a)\) horizontally. Find b if \(a=-1\) and the desired translation is eight units right.
Hint
Use a general point (x,y) to prove the rule for every point.