4.3 I) Enlargement: Fractional Scale Factor
Enlarge the shape below with a scale factor of ½ with the centre of enlargement at (3, 2). Click here for a printable version of the examples in this section.
The first step in answering a scale factor question is to plot the centre of enlargement. We are told in the question that the centre of enlargement is (3, 2) and this is plotted on the graph below:
- The distance between the centre of enlargement and B is 2 left and 4 up. We multiply these distances by ½ to obtain the distance between the centre of enlargement and B’. When we do this, we see that the distance between the centre of enlargement and B’ is 1 to the left and 2 up.
- The distance between the centre of enlargement and C is 2 to the right and 4 up. We multiply these distances by ½ to obtain the distances between the centre of enlargement and C’. This means that the distance between the centre of enlargement and C’ is 1 to the right and 2 up.
We plot these points and connect them to create the enlarged shape (A’B’C).
The shape ABC has been enlarged to create shape A’B’C’. Describe the enlargement.
The scale factor is 1/3. It is worth checking another side on the triangle to see if we have obtained the correct scale factor. I am going to use the sides A’C’ (which has a length of 1 unit) and AC (which has a length of 3 units). We find the scale factor by dividing the length in the enlarged shape by the respective length in the original shape; we divide 1 by 3, which gives us a scale of 1/3, which is exactly the same as the scale factor that we obtained with the other two sides.
We now need to find the centre of enlargement. We are able to do this by drawing lines that connect the respective corners of the original and enlarged shape; we draw lines that connect A to A’, B to B’ and C to C’. We extend the lines past the points that we are connecting. The centre of enlargement is then the point where all of the lines that we have drawn connecting the points intercept one another.
From the diagram above, we can see that all of the lines intercept at the point (7, 2), which means that the centre of enlargement is (7, 2).
Therefore, the answer to this question is an enlargement by a scale factor of 1/3 with a centre of enlargement at (7, 2).