Question 1
Bisect the angle ABC.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
To bisect an angle we need to:
– Place your compass on the point where the two lines meet and draw an arc (blue) that passes through both lines.
– Mark the points where your arc crosses your two starting lines (AB and BC).
– Place your compass on one of the crossing points (green crosses) and draw an arc (green) between your two lines.
Now repeat this step again from the other cross, ensuring your compass is at the same length as before.
– Draw a line (red) passing through the point where the two starting lines (AB and BC) meet and the point where the two green arcs cross.
Question 2
Find the perpendicular bisector to the line AB.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: C
WORKED SOLUTION:
– Set your compasses to a fixed length apart (any length that is more than half the length of the line will do).
– Put your compass at one end of the line and draw an arc (blue).
– With your compasses at the same length, repeat step 2 for the other end of the line (also blue).
– The arcs should cross once one either side of the line. Then, draw a line which passes through the two crossing points. This line (red) is the perpendicular bisector.
Question 3
The points A and B are 8cm apart. Find all the points that are closer to A than B, but within 5cm of A. Shade this region and label it R.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: D
WORKED SOLUTION:
To start, we need to bisect this line, this will give us all the points that are equidistant from A and B.
So, if we want the points closer to A, we are going to want everything left of the red line. But now, we need to also think about all the points that are within 5cm of A, which we can do by setting our compass to 5cm and drawing a circle around A.
So now, we are going to want everything that is in the circle, but also left of red line.
Question 4
Draw the locus of all points that are 1cm away from the shape below.
(Each square here is 1cm)
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B
WORKED SOLUTION:
To find the locus of points that are 1cm away from a corner (a point) we need to draw a circle with radius 1cm away.
To find the points that are 1cm away from a line, we just need to draw parallel lines that are 1cm away from it.
This is all of our points that are 1cm, but some extras… Anywhere that there is overlap, then these points are going to be closer than 1cm, so we need to get rid of those.
Question 5
Jane wishes to put a patio around her house and a pond, a pig pen, and a garage on the grounds of her property.
The grounds of her property are below. The patio must be up against her house and be 1m wide, the pig pen must be 5m \times 5m and in the top left corner, the garage must be 6m \times 4m and in the bottom right corner.
The pond to be within 3m of the location indicated. Each square is 1m \times 1m.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B
WORKED SOLUTION:
Starting off, the pig pen is the easiest to put in as it will just be a 5 \times 5 square.
Next, we can put in the garage.
Although the garage has two different dimensions, we only have one way that it can fit.
Next, we can look at the pond.
We know that to get all points within a certain distance of a centre point, we need to draw a circle with that radius (circle with radius 3 squares here).
Last but not least, we need the patio. The patio will be pretty easy around the sides of the house, as these are just going to be all points between the house and parallel lines that are 1m (1 square) away from it.
We just need to be careful with the corner, remembering that all points within a certain distance of a central point is a circle with that radius (1 square here).
