Enlargements Flashcards

All 6 cards in this deck

What must you state to describe fully an enlargement?

Enlargement, the scale factor, and the centre of enlargement, e.g. enlargement scale factor $3$, centre $(0,2)$.

What are the steps to enlarge a shape by a positive scale factor from a given centre?

e.g. scale factor $2$, centre $(0,1)$

1. Count the steps across and up from the centre to a vertex.
2. Multiply both counts by the scale factor ($\times 2$) and count again from the centre to plot the image vertex.
3. Repeat for every vertex, then join them.

What is the effect of enlarging a shape by a fractional scale factor between $0$ and $1$?

e.g. scale factor $\frac{1}{3}$

The image is smaller than the object and closer to the centre of enlargement, with the same orientation; each length is multiplied by $\frac{1}{3}$.

What is the effect of enlarging a shape by a negative scale factor?

e.g. scale factor $-2$

The image appears on the opposite side of the centre of enlargement and is turned upside down (rotated $180^\circ$), with lengths multiplied by $2$.

True or false? An enlargement of scale factor $-1$ about a point gives the same image as a rotation of $180^\circ$ about that point.

True. Both are accepted as descriptions of that transformation.

True or false? An enlargement changes the angles inside a shape.

False. Angles are unchanged (the shapes are similar); only the lengths are multiplied by the scale factor.