Stage 9 - Q1 - 3 marks
\(A=(0,0)\), \(B=(15,20)\). Find P at \(\frac{1}{5}\) of the way from A to B.
Hint
The fraction is measured from A, not from the origin unless A is the origin.
Stage 9 - Q2 - 3 marks
\(A=(0,0)\), \(B=(2,4)\). Find P at \(\frac{1}{2}\) of the way from A to B.
Hint
The fraction is measured from A, not from the origin unless A is the origin.
Stage 9 - Q3 - 3 marks
\(A=(0,0)\), \(B=(6,3)\), \(P=(4,2)\). What fraction of AB is AP? Give \(AP:PB\).
Hint
\(AP:AB\) and \(AP:PB\) are different ratios.
Stage 9 - Q4 - 3 marks
\(A=(0,0)\) and \(P=(12,9)\). P lies \(\frac{3}{4}\) of the way from A to B. Find B.
Hint
Divide the displacement AP by the given fraction.
Stage 9 - Q5 - 3 marks
Equally spaced points start at \(A=(0,0)\) with step \((2,2)\). Find the point 2 steps from A and the point \(n\) steps from A.
Hint
The starting point is step zero.
Stage 9 - Q6 - 3 marks
\(O=(0,0)\) and \(B=(3,12)\). P is \(\frac{2}{3}\) of the way along OB. A pupil says \(OP:PB\) is 2:3. Correct the claim.
Hint
The two parts of the ratio must add to the whole.
Stage 9 - Q7 - 3 marks
\(A=(0,0)\) and \(P=(1,2)\). P lies \(\frac{1}{3}\) of the way from A to B. Find B.
Hint
Divide the displacement AP by the given fraction.
Stage 9 - Q8 - 3 marks
\(A=(0,0)\), \(B=(12,4)\), \(P=(6,2)\). What fraction of AB is AP? Give \(AP:PB\).
Hint
\(AP:AB\) and \(AP:PB\) are different ratios.
Stage 9 - Q9 - 3 marks
Equally spaced points start at \(A=(0,0)\) with step \((4,3)\). Find the point 5 steps from A and the point \(n\) steps from A.
Hint
The starting point is step zero.
Stage 9 - Q10 - 5 marks
O is the origin. \(P=(6,9)\) lies \(\frac{3}{5}\) of the way to B. Q lies \(\frac{2}{3}\) of the way from O to P. Find B, Q and the ratio \(OQ:QB\).
Hint
Express Q as a fraction of the full segment OB.