3.14.4 Scaling

A scaling transformation changes the size of a figure. The figure is enlarged or reduced by a certain factor, called the scale factor.

• Scaling in mathematics refers to the process of changing the size of a geometric figure by multiplying the coordinates of its points by a factor, known as the scale factor.

• This transformation changes the size of the figure while preserving its shape, orientation, and proportions.

• If the scale factor is greater than \( 1 \), the figure is enlarged, and if it is less than \( 1 \), the figure is reduced. For example, if the scale factor is \( 2 \), all the dimensions of the figure will be doubled, while a scale factor of \( 0.5 \) would shrink the figure to half its size.

• Scaling is commonly used in geometry and coordinate geometry to study properties of shapes, to create similar figures, and to solve problems related to measurements, ratios, and proportions.

• It can also be used in data visualization to create graphs or charts that display numerical data in a visually meaningful way by adjusting the scale of the axes.

Worked example:

On the grid, draw the image of triangle \( A \) after an enlargement by scale factor \( 2 \) ,centre \( ( 7, 3 ) \).

Mark the center \( (7, 3) \)

Draw the lines from the center through the vertices of triangle \( A \).

The scale factor of enlargement is \( 2 \), so use a ruler to measure the lengths of the rays, and double these lengths.

Test yourself

Question 1:

Describe fully the single transformation that maps triangle \( A \) onto triangle \( B \).

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Question 2:

On the grid, draw the image of triangle \( A \) after a translation by the vector \( \frac{-3}{1} \).

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Question 3:

Describe fully the single transformation that maps triangle \( T \) onto triangle \( P \)

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Question 4:

Describe fully the single transformation that maps

shape \( A \) onto shape \( B \)

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Describe fully the single transformation that maps shape \( A \) onto shape \( C \).

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Question 5:

Enlarge triangle \( T \) by scale factor \( -\frac{1}{2} \) with center \( (0,0) \).

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