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Resizing 2D Shapes

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Resizing 2D Shapes

Use the scale factor to multiply every length. Keep your working with each answer. For drawing questions, use the measurements given and label your sides.

Scale factors and properties

1.What does a scale factor tell you to do to the side lengths of a shape?

Multiply every side length by the scale factor
Add the scale factor to every side length
Multiply only the longest side by the scale factor
Change each angle by the scale factor

2.A rectangle is 9 cm long. Find its new length after an enlargement with scale factor 4.

3.A triangle side measures 18 cm. What will its length be after resizing by a scale factor of 1/3?

4.Select every property that stays the same when a 2D shape is resized by a positive scale factor.

The measures of its angles
The lengths of its sides
Its overall shape
Its perimeter
Its orientation
Its area

5.Complete the statement: In a resize, corresponding angles ; corresponding side lengths are multiplied by .

Calculate resized dimensions

6.A square has side length 8 cm. Find its new side length for each scale factor: (a) 3, (b) 1/2, (c) 5, (d) 1/4.

7.At a stargazing event, Tevita sketches a parallelogram with side lengths 12 cm and 20 cm. Calculate both side lengths after a resize by scale factor 1/4.

8.Match each scale factor to its effect on the size of a shape.

Scale factor 2
Scale factor 1/2
Scale factor 1
Scale factor 3
Scale factor 1/5
Scale factor 5

Half the original size
Three times the original size
Five times the original size
Twice the original size
One-fifth the original size
Same size as the original

Draw and explain

9.Draw a right-angled triangle with perpendicular sides 3 cm and 4 cm. Beside it, draw the triangle enlarged by scale factor 2. Label the two corresponding perpendicular sides.

10.Draw a rectangle measuring 8 cm by 6 cm. Draw its image after a resize by scale factor 1/2, and label both dimensions on each rectangle.

Composite shapes and problem solving

11.A composite design has a rectangle 10 cm long and 6 cm wide, with a triangle on top that has base 6 cm and height 4 cm. Find all four measurements after the whole design is enlarged by scale factor 2.

12.Why must every part of a composite figure use the same scale factor if the whole figure is to keep its proportions?

13.Aisha makes a model of a kite at one-quarter the size of the original. The original measures 72 cm by 48 cm. What are the model's dimensions?

14.Write True or False for each statement: (a) A scale factor greater than 1 makes a shape larger. (b) A scale factor of 1 leaves side lengths unchanged. (c) A scale factor between 0 and 1 makes a shape larger. (d) Resizing preserves the measures of the angles.

TrueFalse

15.A shape is enlarged by scale factor 3, then resized again by scale factor 1/2. What is the overall scale factor compared with the starting shape, and is the final shape larger or smaller than the original?