Presentation on theme: "A shape is ‘scaled’ up or down from a given point known as the ‘centre of enlargement’ (C.E.). Distances from this point to the original shape are changed."— Presentation transcript:
A shape is ‘scaled’ up or down from a given point known as the ‘centre of enlargement’ (C.E.). Distances from this point to the original shape are changed by the scale factor to produce the new shape. A B C.E. x 2x In this case the enlargement factor is 2 and the centre is at C.E.
The best way to think of enlargement is to imagine: The larger size being a “picture on a screen”. The smaller size being the “photo slide”. The centre of enlargement being the “projector bulb”. Now imagine light rays from the “bulb” past the small “slide” to the large “screen”. The scale factor is the ratio of sizes of the “pictures”.
With enlargement you can either …….. Work out the scale factor and centre OR the position and size of the new shape.
Draw line connecting the corresponding corners of the two shapes. Extend these beyond the corners. Where the lines cross is the centre of enlargement. The distances are in relation to the scale factor. A B x y A B = y /x B A = x/y C.E.
Draw lines from the centre through the corners of the shape and extend them. Measure the distance from the centre of enlargement (C.E.) to a corner and multiply this by the scale factor. The new corner is this distance from the centre. Repeat this for each of the other corners. x y B A C.E.
Enlargement works two ways; If the scale factor is less than one (a fraction), then the new shape is smaller than the original. If the scale factor is greater than one then the new shape is bigger.
Another type of question associated with enlargement is one using SIMILAR triangles. 6cm 9cm 10cm You are then asked to work out the lengths of the missing sides
6cm 9cm 12cm Going from the small to the large, what multiplication factor changes 6cm to 9cm? x 1.5 1.5 So, multiplying the 9cm side on the small triangle gives us 13.5cm 9 x 1.5 13.5cm If we multiply to go from small to large, then we divide if going from large to small. So the remaining side of the small triangle is 12 ÷ 1.5 12 ÷ 1.5 8cm
If you are given a shape like this… Just redraw it as two separate triangles and work out the missing lengths!! To find the length (?) all you need to do is subtract the length of the smaller triangle from the larger triangle. ? 20 cm 8 cm 12 cm 6 cm