12.1.5 Negative Enlargements - Cardiff Tutor Company

Question 1

LEVEL 6

Enlarge the following shape by a scale factor of $-2$ about the origin

Which diagram gives the correct enlargement of the shape?

CORRECT ANSWER: B

WORKED SOLUTION:

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 (blue) shape.

We’ll start with looking at the nearest corner to the origin.

If we break this up, we can see that we go right $1$ and up $1$ .

If we follow our usual rule for enlarging (and since this is a negative enlargement) , we’ll have to go left $2$ and down $2$ 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 2

LEVEL 6

Shape $A$ is enlarged about the origin. The new shape is shape $B$ .

What is the scale factor of enlargement of shape $A$ onto shape $B$ ?

Select the correct from the list below:

A: $-2$

B: $-1$

C: $-3$

D: $2$

CORRECT ANSWER: A: $-2$

WORKED SOLUTION:

Draw lines back from the points of shape $A$ , through the origin, then to the corresponding points of shape $B$ .

We then 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 3

LEVEL 6

Shape $A$ is enlarged about a point. The new shape is shape $B$ .

What is the scale factor of enlargement of shape $A$ onto shape $B$ and the point of enlargement?

Select the correct from the list below:

A: $-\frac{1}{2}$ and $(-1,-1)$

B: $-\frac{1}{2}$ and $(0,0)$

C: $\frac{1}{2}$ and $(-1,-1)$

D: $-2$ and $(-1,-1)$

CORRECT ANSWER: A: $-\frac{1}{2}$ and $(-1,-1)$

WORKED SOLUTION:

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 $(-1,-1)$

We then 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 half the distance from the origin than the corresponding points on shape $A$ .

However, $\frac{1}{2}$ 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 $-\frac{1}{2}$

Question 4

LEVEL 6

Shape $A$ is enlarged about a point. The new shape is shape $B$ .

The scale factor of enlargement of shape $A$ onto shape $B$ is $- 1.5$

What is the point of enlargement?

Select the correct from the list below:

A: $(1,1)$

B: $(0,0)$

C: $(1,0)$

D: $(0,1)$

CORRECT ANSWER: A: $(1,1)$

WORKED SOLUTION:

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 $(1,1)$ , therefore the point of enlargement is $(1,1)$

Question 5

LEVEL 6

Enlarge the following shape by a scale factor of $-2$ about the point $(-1,0)$

Which diagram gives the correct enlargement of the shape?

Select the correct from the list below:

CORRECT ANSWER: A:

WORKED SOLUTION:

Draw lines back from the points of shape $A$ , through the point $(-1,0)$ , then to the edges of the graph.

We can then see that there are four points that lie on the grey lines in the bottom left quadrant, that form a square of width $2$ .

Therefore our points are $(-3,0), (-3,-2), (-5,-2)$ , and $(-5,0)$