Normally, when you are enlarging an object in GCSE Maths, you have to be able to enlarge from a given point.
Previously, we discussed how to enlarge from a point. Today, we will be looking at fractional scale factors.
What does a fractional scale factor do?
Scale factors that are larger than 1 will make a shape larger
Scale factors between 0 and 1 will make an object smaller.
Example 1: Enlarge the shape by a scale factor of 1/2 about the point (2,1)
Step 1: Draw the centre of enlargement on the grid.
Doing this means you wont forget where you're enlarging from.
Step 2: Find the movement from the centre to one of the points on the shape.
We can see that to get to the bottom left corner, we move 2 right and 4 up
Step 3: Multiply this movement by the Scale Factor.
Our scale factor is 1/2, so this movement halves to 1 right and 2 up.
Step 4: Plot this point on the diagram.
When you are plotting this point, it is vital that you count from the centre of enlargement.
Step 5: Repeat steps 2 - 4 for the other corners of the shape.
Step 6: Draw the enlarged shape and label the image and enlargement.
Example 2: Shape A is enlarged to shape A'. Find the scale factor and centre of enlargement.
Finding the Scale Factor.
All we have to do here is to look at one of the pairs of sides. If we use the bottom of each shape, shape A is 3cm long and shape A' is 1 cm long.
This gives a scale factor of 1/3.
Finding the centre of enlargement.
To find this, we join up two pairs of matching corners with striaght lines and see where they join up.
We can see here that the two lines join up at the point (1,0). This is the centre of enlargement.