Dilations 8-1

Determine whether the dilation from the figure on the left to the figure on the right is an enlargement or a reduction. Then, find the scale factor.

• Reduction; 3

• Enlargment; 1/3

• Reduction; 1/3

• Enlargment; 3

Answer explanation

This is an enlargement because the new shape is bigger than the old one. To find the scale factor, divide the new side length (18) by the old one (6) and simplify (18/6 = 3).

Determine whether the dilation from the figure on the left to the figure on the right is an enlargement or a reduction. Then, find the scale factor.

• Reduction; 1/6

• Enlargment; 6

• Reduction; 1/2

• Enlargment; 2

Answer explanation

This is a reduction because the new shape is smaller than the original. To find the scale factor, divide the new side length (6) by the old one (12) and simplify (1/2).

Determine whether the dilation from the figure on the left to the figure on the right is an enlargement or a reduction. Then, find the scale factor in simplest form.

• Reduction; 1/6

• Reduction; 1/9

• Reduction; 1/3

• Reduction; 2/3

Answer explanation

To find the scale factor, divide the new side length (6) by the old one (9) and simplify (2/3)

Determine whether the dilation from the figure on the left to the figure on the right is an enlargement or a reduction. Then, find the scale factor.

• Enlargement; 8/5

• Enlargement; 3

• Enlargement; 5/8

• Enlargement; 1/3

Answer explanation

Take the new side length (8) and divide it by the old one (5). So, we get 8/5!

Graph points D, F, and G.

• 
• 

Answer explanation

The x coordinate comes first, then y.

Based on the scale factor, is this an enlargement or a reduction?

• Enlargement

• Reduction

• Not enough information

Answer explanation

If k < 1, then the dilation is a reduction.

Find the coordinates of D' (the "new" D).

• D'(3, 4)

• D'(4, 3)

• D'(3, 3)

• D'(3.25, 3.25)

• D'(4.75, 4.75)

Answer explanation

Multiply k by the coordinates of D to get the coordinates of D'.

Find the coordinates of F' (the "new" F).

• F'(0, 0)

• F'(0.75, 0.75)

• F'(-0.75, -0.75)

• F'(0, 3)

• F'(3, 0)

Answer explanation

Multiply k by the coordinates of F to get the coordinates of F'.

Find the coordinates of G' (the "new" G).

• G'(0, 6)

• G'(6, 6)

• G'(0, 0)

• G'(8.75, 0.75)

• G'(6, 0)

Answer explanation

Multiply k by the coordinates of G to get the coordinates of G'.

Based on the picture, is this an enlargement or a reduction?

• Enlargement

• Reduction

• Not enough information

Answer explanation

The new triangle is smaller than the original, then the dilation is a reduction.