Enlargements (Leaving Cert Mathematics): Flashcards

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Enlargements
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Definition of enlargement

Transformation changing size, keeping proportions the same

Object in enlargement

The original shape before transformation

Image in enlargement

The new shape after the enlargement

Centre of enlargement

Fixed point from which the enlargement takes place

Scale factor definition

Number showing how many times bigger/smaller image is than object

Scale factor formula

rac{ ext{image side}}{ ext{object side}}

Length of image side formula

Image side =kimes= k imes object side

Two requirements to draw enlargement

Centre of enlargement and scale factor

Vertex as centre of enlargement

That vertex doesn't move, stays in same position

Scale factor <1< 1 produces

Smaller figure (reduction)

Scale factor >1> 1 produces

Bigger figure (true enlargement)

How to find centre of enlargement

Join corresponding vertices, extend lines until they meet

Area of image in enlargement

k2imesk^2 imes area of object

Inverse enlargement scale factor

rac{1}{k} where kk is original scale factor

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