Stage 9 - Q1 - 3 marks
\(A=(-2,-1)\), \(B=(13,19)\). 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
\(A=(-3,2)\), \(B=(-1,6)\). 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
\(A=(2,0)\), \(B=(8,3)\), \(P=(6,2)\). What fraction of AB is AP? Give \(AP:PB\).
Hint
\(AP:AB\) and \(AP:PB\) are different ratios.
Stage 9 - Q4 - 3 marks
\(A=(1,3)\) and \(P=(13,12)\). 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
\(A=(0,1)\), \(B=(10,11)\). A pupil multiplies B by \(\frac{2}{5}\) to locate P from A. Explain and correct this method.
Hint
The starting point contributes to the final position.
Stage 9 - Q6 - 3 marks
Equally spaced points start at \(A=(-1,-2)\) with step \((3,4)\). Find the point 4 steps from A and the point \(n\) steps from A.
Hint
The starting point is step zero.
Stage 9 - Q7 - 3 marks
\(A=(-2,1)\) and \(P=(-1,3)\). 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
\(A=(-3,-1)\), \(B=(9,3)\). A pupil multiplies B by \(\frac{1}{2}\) to locate P from A. Explain and correct this method.
Hint
The starting point contributes to the final position.
Stage 9 - Q9 - 3 marks
\(A=(2,2)\), \(B=(22,17)\), \(P=(14,11)\). What fraction of AB is AP? Give \(AP:PB\).
Hint
\(AP:AB\) and \(AP:PB\) are different ratios.
Stage 9 - Q10 - 5 marks
\(P=(3,5)\) is one third of the way from A to B. \(Q=(7,8)\) is two thirds of the way from A to B. Find A and B without assuming A is the origin.
Hint
The points divide AB into three equal steps.