Stage 8 - Q1 - 2 marks
M is the midpoint of AB, where \(AB=12.8\) cm. Find AM.
Hint
Equal compass radii produce points with equal distances from both endpoints.
Stage 8 - Q2 - 2 marks
M is the midpoint of AB, where \(AB=13.9\) cm. Find AM.
Hint
Equal compass radii produce points with equal distances from both endpoints.
Stage 8 - Q3 - 3 marks
P lies on the perpendicular bisector of AB and \(PA=9.5\) cm. Find PB and explain.
Hint
Equal compass radii produce points with equal distances from both endpoints.
Stage 8 - Q4 - 3 marks
P lies on the perpendicular bisector of AB and \(PA=5.2\) cm. Find PB and explain.
Hint
Equal compass radii produce points with equal distances from both endpoints.
Stage 8 - Q5 - 4 marks
On separate plain paper, draw \(AB=5.3\) cm and construct its perpendicular bisector with ruler and compasses. State two checks of your construction.
Hint
Equal compass radii produce points with equal distances from both endpoints.
Stage 8 - Q6 - 4 marks
On separate plain paper, draw \(AB=6.4\) cm and construct its perpendicular bisector with ruler and compasses. State two checks of your construction.
Hint
Equal compass radii produce points with equal distances from both endpoints.
Stage 8 - Q7 - 5 marks
A pupil chooses a compass radius 3 cm to bisect an 8 cm segment. Explain why the arcs fail and give a valid radius.
Hint
Compare the radius with half the segment length.
Stage 8 - Q8 - 5 marks
A point P has \(PA=5.2\) cm and \(PB=5.0\) cm. Could P lie on the perpendicular bisector of AB if these are exact lengths?
Hint
Use the defining equal-distance property.
Stage 8 - Q9 - 5 marks
Two points P and Q are each equidistant from A and B. P and Q are distinct. Explain why the whole line PQ is the perpendicular bisector of AB.
Hint
Locate both points using the same equal-distance condition.
Stage 8 - Q10 - 5 marks
Construct a right triangle with \(AB=6\) cm, \(AC=8\) cm and angle \(A=90\)°. Construct the perpendicular bisectors of AB and AC. Their intersection is O. Explain why O is equally distant from all three vertices, then draw the circle through them and measure its radius.
Hint
Use one equal-distance statement from each perpendicular bisector.