Normally, when you are enlarging an object in GCSE Maths, you have to be able to enlarge from a given point.
Imagine putting your hands in front of a lamp and making a shadow.
The lamp is the centre of enlargement, your hand is the object and the shadow of your hand on the wall is the enlarged image.
What is a negative scale factor.
A negative scale factor means you have to do something strange with the points.
If you had a scale factor of 2, you would enlarge a point by doubling the movement from centre point.
i.e. if you had a movement of 2 right and 3 up. You would double this to make 4 right and 6 up.
If you have a negative scale factor, you swap the direction of the movement.
i.e for a scale factor of -2. if you had a movement of 2 right and 3 up. You would double this, and change the direction, to make 4 left and 6 down.
Example 1: Enlarge the shape by a scale factor of -2 about the point (1,0)
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 1 right and 2 up
Step 3: Multiply this movement by the Scale Factor.
Our scale factor is -2, so this movement doubles and changes direction to 2 left and 4 down.
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 B. 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 top of each shape, shape A is 1cm long and shape B is 3 cm long.
Because the centre is between the shapes and the shape has turned around , we must have a negative scale factor
This gives a scale factor of -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.
You need to be really careful that you match up the correct pairs of coners, remember that the shape has flipped upside down.
We can see here that the two lines join up at the point (1,1). This is the centre of enlargement.