Usually, when we are enlarging an object in maths, we can enlarge from** a given point**.

For example, imagine putting your hands in front of a lamp and making a shadow.

In this scenario, 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**.

Let's look at this process of enlargement from a given point in action now in some examples.

**e.g. Enlarge the shape shown below by a scale factor of 2 about the point (1,0).**

**Step 1:** Draw the centre of enlargement on the grid (so we won't forget where we are 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 of the rectangle from the centre, we need to move **1 square to the right and 2 up**.

**Step 3: **Multiply this movement by the scale factor:

Our scale factor is **2**, so this movement doubles to become **2 squares to the right and 4 up**.

**Step 4:** Plot this point on our diagram (when we are doing this, it is vital to count from the centre of enlargement** not **the origin):

**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:

**e.g. Shape a has been enlarged to become shape b. Find the scale factor and centre of enlargement.**

**Finding the scale factor**

We need to look closely at one of the pairs of sides.

If we use the horizontal base of each square, shape a is **1 square long** and shape b is **3 squares long**.

This means that our scale factor is **3**.

**Finding the centre of enlargement**

To find this, we need to join up two pairs of matching corners with straight lines and see where they cross:

We can see here that the two lines cross at the point **(1,1)**, so this is our centre of enlargement.

In this activity, we will enlarge shapes from a given point by applying a scale factor, as well as find the centre of enlargement and scale factor after an enlargement has occurred.

You may find it helpful to have a pencil and some squared paper handy to support you in this activity. If you do not, you will need to be able to visualise these enlargements in your mind's eye.