Question 1
Which shape enlarges Shape X by scale factor -1 with centre of enlargement (0,0)?
ANSWER: Multiple Choice (Type 1)
A: Shape A
B: Shape B
C: Shape C
Answer: A
Workings:
Draw two ray lines, one passing through the point (4,2) and the other (1,4), with both crossing the origin.
Because the scale factor of enlargement is negative, the new shape must be in the opposite quadrant.
As Shape X is enlarged with centre of enlargement (0,0), each point on it is simply multiplied by -1 to get the new coordinates.
This means the points (1,4) and (4,2) on X will map to (-1,-4) and (-4,-2) respectively on the new shape.
Therefore the new shape must be Shape A.
Marks = 3
Question 2: [3 marks]
Enlarge the following shape by a scale factor of -2 about the origin.
Which diagram gives the correct enlargement of the shape?
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A
WORKING:
To start, we need to find our point of enlargement which is the origin, (0,0).
We now need to draw a line from the origin to each corner of the original (grey) shape.
We’ll start with looking at the nearest corner to the x axis.
If we break this up, we can see that we go right 3 and up 1 from the origin.
If we follow our usual rule for enlarging (and since this is a negative enlargement) , we’ll have to go left 6 and down 2 from the origin, to get the corresponding point of the new shape.
Repeating the process for the other points and drawing the new shape will give us a diagram like this:
Question 3: [3 marks]
Enlarge the following shape by a scale factor of -\dfrac{1}{3} about the point (-2,1)
Which diagram gives the correct enlargement of the shape?
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A
WORKING:
To start, we need to find our point of enlargement which is (-2,1).
We now need to draw a line from (-2,1) to each corner of the original (grey) shape.
We’ll start with looking at the nearest corner to the point of enlargement.
If we break this up, we can see that we go right 3 and up 0 from (-2,1)
If we follow our usual rule for enlarging (and since this is a negative enlargement) , we’ll have to go left 6 and down 0 from (-2,1), to get the corresponding point of the new shape.
Repeating the process for the other points and drawing the new shape will give us a diagram like this:
Question 4:
Shape A is enlarged about a point. The new shape is shape B.
Question 4(a): [1 mark]
What is the point of enlargement?
Answer type: Multiple choice type 1
A: (-1,0)
B: (0,-1)
C: (0,0)
D: (0,1)
ANSWER: A: (-1,0)
WORKING:
Draw lines back from the points of shape A to the corresponding points of shape B.
We can that the lines cross at the point (-1,0)
Question 4(b): [1 mark]
What is the scale factor of enlargement of shape A onto shape B
Answer type: Simple text answer
ANSWER: -2
WORKING:
We count the number of times we go left and down from the origin to each point on shape B.
We compare this to the number of times we go up and right to the corresponding points on shape A.
We can see that the points on shape B are twice the distance from the origin than the corresponding points on shape A.
However, 2 is not our scale factor of enlargement, since shape B is on the opposite side of the point of enlargement.
Hence, our enlargement is a negative enlargement, which is - 2
Question 5:
Calculate the scale factor of enlargement of each enlargement that transforms shape A onto shape B, when:
Question 5(a): [1 mark]
the centre of enlargement is the origin, and the shapes A and B are as follows:
Answer type: Simple text answer
ANSWER: -4
WORKING:
We see that to get to the point closest to the origin on shape A, we move right 1 and up 1 from the origin.
To get to the corresponding point on shape B, we move left 4 and down 4 from the origin.
We repeat this process for all points on each shape.
Therefore, since shape B is in the negative quadrant of the graph, and is 4 times as big as shape A and 4 times further away from the point of enlargement than shape A, the scale factor that transforms shape A onto shape B is -4
Question 5(b): [1 mark]
the centre of enlargement is (0,-1), and the shapes A and B are as follows:
Answer type: Simple text answer
ANSWER: -1
WORKING:
We see that to get to the point closest to (0,-1) on shape A, we move right 0 and up 1 from (0,-1)
To get to the corresponding point on shape B, we move left 0 and down 1 from (0,-1)
We repeat this process for all points on each shape.
Therefore, since shape B is in the negative quadrant of the graph, and is the same size as shape A and the same distance away from the point of enlargement, the scale factor that transforms shape A onto shape B is -1
Question 5(c): [1 mark]
the centre of enlargement is (-2,-2), and the shapes A and B are as follows:
Answer type: Multiple choice type 1
A: - \dfrac{1}{2}
B: - \dfrac{1}{3}
C: \dfrac{1}{2}
D: -2
ANSWER: A: - \dfrac{1}{2}
WORKING:
We see that to get to the point closest to (-2,-2) on shape A, we move right 2 and up 2 from (-2,-2)
To get to the corresponding point on shape B, we move left 1 and down 1 from (-2,-2)
We repeat this process for all points on each shape.
Therefore, since shape B is in the negative quadrant of the graph, and is half the size of shape A and half distance away from the point of enlargement than shape A, the scale factor that transforms shape A onto shape B is - \dfrac{1}{2}
Question 6: [3 marks]
Enlarge the following shape by a scale factor of -3 about the point (2,3)
Which diagram gives the correct enlargement of the shape?
Answer type: Multiple choice type 1
A: 
B: 
C: 
D: 
ANSWER: A
WORKING:
To start, we need to find our point of enlargement which is (2,3).
We now need to draw a line from (2,3) to each corner of the original (grey) shape.
We’ll start with looking at the nearest corner to the y axis.
If we break this up, we can see that we go right 0 and up 1 from (2,3)
If we follow our usual rule for enlarging (and since this is a negative enlargement) , we’ll have to go left 0 and down 3 from (2,3), to get the corresponding point of the new shape.
Repeating the process for the other points and drawing the new shape will give us a diagram like this:
