Scale Factor

Scale Factor Scale factor = new measurement old measurement Old measurement x Scale factor = new measurement Scale factor more than 1 => shape gets bigger (Enlargement) Scale factor less than 1 => shape gets smaller (Reduction) Congruent shapes are similar shapes with SF = 1

Reductions, Enlargements and the Scale Factor Triangle ABC needs to be enlarged by a scale factor of 3. What do we need to do first? What do we need to do second? 4 5 B 3 C

What do you notice about the new drawing? What about its ‘name’? The new triangle is called ________ with side lengths: A’B’ = _______ B’C’ = _______ A’C’ = _______ A 4 5 B 3 C

Triangle JKL needs to be reduced by a scale factor of 0.5. What are the new side lengths of triangle J’K’L’? 9 4 K 8 L

So Triangle J’K’L’ now looks like this: 9 4 J’K’ = 4 x ________ K’L’ = 8 x ________ J’L’ = 9 x _________ So Triangle J’K’L’ now looks like this: 9 4 K 8 L

Determining Scale Factor 24 cm x 4 A 6 cm x 4 8 cm 2 cm I C x 4 20 cm B 5 cm H These two triangles are similar because the ratio of corresponding sides is the same. To find the scale factor can you determine what factor was multiplied by a side length to create the corresponding side length? The scale factor from the small triangle to the larger triangle is 4! The scale of the drawing can be written as 1cm : 4 cm

Determining Scale Factor W R x ½ 20 ft 10 ft x ½ 8 ft 16 ft V M 6 ft x ½ H B 12 ft What was the scale factor used to create the smaller triangle? What type of factor creates a smaller product? The scale factor used is ½ or 0.5. The scale of the drawing can be written as 2 feet:1 foot

Using Scale Factor to Solve for Missing Side Lengths Solve for the missing side GH. T F 3 ft 15 ft 4 ft H V 20 ft 10 ft G U Determine the scale factor… The scale of the drawing is: Now multiply the scale factor by the original side… If you cannot determine the scale factor divide:

If two objects are similar then one is an enlargement of the other The rectangles below are similar: Find the scale factor of enlargement that maps A to B A B 8 cm 16 cm 5 cm 10 cm Not to scale! Scale factor = x2 Note that B to A would be x ½

If two objects are similar then one is an enlargement of the other The rectangles below are similar: Find the scale factor of enlargement that maps A to B A B 8 cm 12 cm 5 cm 7½ cm Not to scale! Scale factor = x1½ Note that B to A would be x 2/3

8 cm If we are told that two objects are similar and we can find the scale factor of enlargement then we can calculate the value of an unknown side. A B 3 cm Not to scale! 24 cm x cm Comparing corresponding sides in A and B: 24/8 = 3 so x = 3 x 3 = 9 cm

5.6 cm If we are told that two objects are similar and we can find the scale factor of enlargement then we can calculate the value of an unknown side. A B 2.1 cm Not to scale! x cm 7.14 cm Comparing corresponding sides in A and B: 7.14/2.1 = 3.4 so x = 3.4 x 5.6 = 19.04 cm

Scale Factor applies to ANY SHAPES that are mathematically similar. 1.4 cm 7 cm 2cm y z 3 cm 15 cm 6 cm Given the shapes are similar, find the values y and z ? 3 15 5 1 Scale factor = ESF = = 5 Scale factor = RSF = = 0.2 y is 2 x 5 = 10 z is 6 x 0.2 = 1.2

Scale factors www.mathsrevision.com Enlargement Scale factor? 3 2 ESF = = 8 8 8cm 12 12cm 12 Reduction Scale factor? www.mathsrevision.com 2 3 5cm RSF = = 7.5cm Can you see the relationship between the two scale factors?

Scale factors a 9cm 27cm www.mathsrevision.com 5cm b 15cm Find a given ESF = 3 a 9 ESF = 3 = 9cm 27cm a By finding the RSF Find the value of b. www.mathsrevision.com 5cm b 1 3 b 15 5 15 RSF = = = 15cm