Question
(a) Measure the size of angle x.
(b) Measure the length of line AB in millimetres.
(c) Mark the midpoint, M, of line AB.
(d) Draw a line through the point M that is perpendicular to line AB.
▶️Answer/Explanation
(a) $46^{\circ}$
(b) $84$
(c) Mid-point marked $42$ mm along $AB$ from $A.$
(d) Line at $90^{\circ}$ to $AB$ at $M.$
(a) Measure the size of angle \( x \):
1. Use a protractor.
2. Place the midpoint of the protractor at point A.
3. Align the baseline with line AB.
4. Read the angle where line AC intersects the protractor scale.
(b) Measure the length of line AB:
1. Use a ruler, preferably one with millimeters for precision.
2. Place the ruler along line AB.
3. Record the length in millimeters.
(c) Mark the midpoint \( M \) of line AB:
1. Find the midpoint by dividing the length of AB by 2.
2. Mark this point M.
(d) Draw a line through point M that is perpendicular to AB:
1. Use a ruler and a set square.
2. Place the set square’s right angle at point M.
3. Draw a straight line through M, perpendicular to AB.
Question
The diagram shows a circle, centre O.
P lies on the circle.
(a) Write down the mathematical name of the line OP.
(b) Draw a tangent to the circle at P.
▶️Answer/Explanation
Ans:
(a) radius
(b) Ruled line drawn through P perpendicular to OP
(a)
- The line OP goes from the center of the circle (O) to a point on the circle (P).
- This line is called the radius of the circle.
(b)
- A tangent is a straight line that touches the circle at exactly one point.
- At point P, the tangent would be a straight line that just touches the circle without crossing it.
- The radius (OP) is always perpendicular to the tangent at point P.
Question
AB is the diameter of a circle.
C is a point on AB such that AC = 4cm.
(a) Using a straight edge and compasses only, construct
(i) the locus of points which are equidistant from A and from B,
(ii) the locus of points which are 4 cm from C.
(b) Shade the region in the diagram which is
• nearer to B than to A
and
• less than 4 cm from C.
Answer/Explanation
(a) 
(b)
Question
(a) Using a straight edge and compasses only, construct the perpendicular bisector of AB.
Show all your construction arcs.
(b) Draw the locus of points that are 4 cm from A.
(c) Shade the region which is less than 4 cm from A and nearer to B than to A.
Answer/Explanation
(a)Perpendicular bisector drawn with 2 pairs of arcs and ruled
(b) Circle drawn radius 4cm
(c)Correct region shaded
Question
Triangle ABC has sides AB = 40m, BC = 25m and AC = 35m.
Using a scale of 1 cm to represent 5m, construct triangle ABC.
The construction must be completed using a ruler and compasses only.
All construction arcs must be clearly shown.
Answer/Explanation
Ans: Triangle drawn correctly with ruler and arcs
Question
(a) On the diagram above, draw a line perpendicular to the line AB, through the point P.
(b) Using a straight edge and compasses only, construct the locus of points that are equidistant
from A and from C.
Answer/Explanation
Ans:
(a) Ruled perpendicular line
through P
(b) Correct ruled line drawn
with 2 correct sets of arcs