Stage 8 - Q1 - 2 marks
Find the midpoint of \((2,4)\) and \((8,6)\).
Hint
Average each coordinate separately.
Stage 8 - Q2 - 2 marks
Find the midpoint of \((-6,2)\) and \((4,-4)\).
Hint
Keep the signs when adding coordinates.
Stage 8 - Q3 - 2 marks
Find the midpoint of \((1,2)\) and \((6,7)\).
Hint
A midpoint need not have integer coordinates.
Stage 8 - Q4 - 2 marks
The segment from \((3,-5)\) to \((3,7)\) is vertical. Find its midpoint and explain which coordinate stays unchanged.
Hint
Use the geometry to check your arithmetic.
Stage 8 - Q5 - 3 marks
A is \((-2,5)\) and midpoint M is \((3,1)\). Find the other endpoint B.
Hint
The displacement from A to M repeats from M to B.
Stage 8 - Q6 - 3 marks
Opposite corners of a rectangle are \((-4,-1)\) and \((6,7)\). Find its centre.
Hint
A rectangle’s centre is the midpoint of a diagonal.
Stage 8 - Q7 - 4 marks
A quadrilateral has vertices A\((0,1)\), B\((4,2)\), C\((6,7)\) and D\((2,6)\) in order. Show that its diagonals share a midpoint.
Hint
Opposite vertices determine the diagonals.
Stage 8 - Q8 - 4 marks
A is \((a,2)\) and B is \((8,b)\). Their midpoint is \((5,-1)\). Find a and b.
Hint
The two coordinate equations are independent.
Stage 8 - Q9 - 5 marks
M is the midpoint of AB and N the midpoint of AM. If A is \((2,-2)\) and N is \((5,1)\), find M and B.
Hint
Work outward from the smaller segment.
Stage 8 - Q10 - 6 marks
The midpoints of AB, BC and CA are \((2,1)\), \((5,3)\) and \((1,4)\) respectively. Find A, B and C.
Hint
Write each midpoint as half the sum of two vertices and look for cancellation.