Stage 8 - Q1 - 3 marks
Translate P by \(\binom{3}{-2}\).
Hint
Add three to x and subtract two from y.
Stage 8 - Q2 - 3 marks
Translate P by \(\binom{-4}{5}\).
Hint
Add the vector entries to their corresponding coordinates.
Stage 8 - Q3 - 4 marks
Translate triangle ABC by \(\binom{2}{3}\).
Hint
Move every vertex two right and three up.
Stage 8 - Q4 - 2 marks
A translation maps \((2,-3)\) to \((-4,5)\). Find its vector.
Hint
The vector describes the change, not the final position.
Stage 8 - Q5 - 3 marks
A translation by \(\binom{5}{-7}\) gives image \((1,2)\). Find the original point.
Hint
Undo both coordinate changes.
Stage 8 - Q6 - 4 marks
A horizontal segment has endpoints \((-1,2)\) and \((4,2)\). Translate it by \(\binom{3}{-5}\) and show that its length is unchanged.
Hint
Compare the difference between endpoints before and after.
Stage 8 - Q7 - 4 marks
Combine translations \(\binom{4}{-3}\) and \(\binom{-6}{8}\). Does their order change the final image?
Hint
Addition of each pair of components is commutative.
Stage 8 - Q8 - 4 marks
P\((3,-2)\) is translated by \(\binom{a}{4}\) to a point on the line \(x=9\). Find a and the image.
Hint
Use the line equation as a coordinate condition.
Stage 8 - Q9 - 5 marks
Three translations return every point to its start. Two vectors are \(\binom{5}{-1}\) and \(\binom{-2}{6}\). Find the third vector and justify it.
Hint
The total vector must be zero.
Stage 8 - Q10 - 6 marks
Triangle A\((1,2)\), B\((4,2)\), C\((1,5)\) is translated. The midpoint of AA′ is \((4,-1)\). Find the translation vector and all three image vertices.
Hint
Use the midpoint information before considering B and C.