Dilations

Dilations Practice

Multiple Choice

Triangle ABC is dilated to produce triangle A'B'C' with scale factor 3/4 . Which describes the relationship between the two triangles?

• Triangle A'B'C' is an enlargement of triangle ABC

• Triangle A'B'C' is a reduction of triangle ABC

• Triangle A'B'C' is a mirror image of triangle ABC

Scale Factor is represented by the letter k

• When k > 1, the shape is enlarged (gets bigger)

• When k < 1, the shape is reduced (get smaller)

• When k = 1, the shape stays the same

Multiple Choice

Which is true about the scale factor when a figure is enlarged?

• The scale factor is zero.

• The scale factor is 1.

• The scale factor is larger than 1.

• The scale factor is smaller than 1.

Dilations create Similar Figures

• Corresponding angles are congruent

• Corresponding sides are proportional

• Since sides are proportional, we can write an equivalent proportion

Multiple Choice

Triangle PQR is similar to triangle DEF shown. Which describes the relationship between the corresponding sides of the two triangles?

Multiple Choice

• A

• B

• C

• D

Now Let's Practice more Dilation Rules

• Remember: dilation rules are the ONLY rule where x and y are MULTIPLIED by a coefficient

• Dilation rules will always look like this, where k is the scale factor:

• (x, y) --> (kx, ky)

Multiple Choice

Which of the following is the algebraic representation for a dilation?

• (x, y) → (x, 3y)

• (x, y) → (3x, 3y)

• (x, y) → (x, y - 3)

• (x, y) → (.5x, .4y)

Multiple Choice

• F

• G

• H

• J

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• F

• G

• H

• J

Multiple Choice

• A

• B

• C

• D

Dilations also affect perimeter and area!

Make sure to find the perimeter/area before and after the dilation, then compare! It may help to draw a picture!

Multiple Choice

Rectangle ABCD has a length of 6 and a height of 5. It is dilated by a scale factor of 3.

What is true about the perimeter of A'B'C'D', the new rectangle?

• The perimeter of A'B'C'D' is the same as the perimeter of ABCD

• The perimeter of A'B'C'D' is the 3 times larger than the perimeter of ABCD

• The perimeter of A'B'C'D' is the 6 times larger than the perimeter of ABCD

• The perimeter of A'B'C'D' is the 9 times larger than the perimeter of ABCD

Multiple Choice

A triangle has a perimeter of P units. The triangle is dilated by a scale factor of 1/2.

Which expression could represent the perimeter of the new shape?

• $\frac{1}{4}P$ units

• $\frac{1}{2}P$ units

• 2P units

• 4P units

Multiple Choice

Jane's garden is a 2 ft x 3 ft rectangle. If she increases it by a scale factor of 3, what is the new area of her garden?

• 72 square feet

• 18 square feet

• 36 square feet

• 54 square feet

Multiple Choice

A rectangle is dilated by a scale factor of 2.

What happens to the area?

• doubles

• triples

• quadruples

• not enough information