Dilations and Similarity of Figures

Dilations & Similarity

Multiple Choice

A dilation is which of the following:

• only an enlargement

• only a reduction

• either an enlargement or a reduction

• neither an enlargement nor a reduction

Multiple Choice

A dilation always produces a congruent figure.

• True

• False

Multiple Choice

A dilation always produces a similar figure. Similar figures have the same ______ but different ______.

• measure; shapes

• sizes; shapes

• value; measures

• shape; sizes

Multiple Choice

Did the image enlarge, reduce or none of the above?

• Enlarge

• Reduce

• None of the above

Multiple Choice

Does the image show a Dilation? If yes, did the image enlarge, reduce or none of the above?

• Yes, enlarge

• Yes, reduce

• No

Multiple Choice

Under a dilation, which scale factor will result in a congruent image?

• -2

• 0

• 1

• ¹/₂

Multiple Choice

An image is dilated at a scale factor of 1.5. This means the dilation is an enlargement and the dilated image will be bigger.

• True

• False

Multiple Choice

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

• B' (2 , 4.5)

• B' (-8 ,-18)

• B' (8 ,18)

• B' (9 ,4)

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

Multiple Choice

How do you write the algebraic notation when the scale factor is 3?

• (x, y) goes to (1/3x, 1/3y)
• (x, y) goes to (-3x, -3y)
• (x, y) goes to (x + 3, y + 3)
• (x, y) goes to (3x, 3y)

Multiple Choice

Dilate the figure by a scale factor of 3. What are the coordinates of the image?

A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

Multiple Choice

Dilate Point B by a scale factor of 3:

• (12,0)
• (12,12)
• (4,3)
• (0,12)

Multiple Choice

Triangle ABC will be dilated by a scale factor of 1/2.  What will be the coordinates of C'?

• (-1, -2.5)
• (12, 6)
• (3, -1.5)
• (0, 1.5)

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's a reduction; the scale factor is 2.
• It's an enlargement; the scale factor is 2.
• It's an enlargement; the scale factor is 1/2.
• It's a reduction; the scale factor is 1/2.

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's an enlargement; the scale factor is 1/2.
• It's an enlargement; the scale factor is 2.
• It's a reduction; the scale factor is 1/2.
• It's a reduction; the scale factor is 2.

Multiple Choice

Trapezoid A’B’C’D’ is the dilation of trapezoid ABCD.

Which algebraic representation shows this dilation?

• (x, y) --> (2x, 2y)

• (x, y) --> (0.5x, 0.5y)

• (2x, 2y) --> (x, y)

• (x, y) --> (3x, 2y)

Multiple Choice

Does the image show a Dilation and what is the scale factor?

• Yes; k = 2

• Yes; k = 1/2

• No, it's a translation.

• No, it's a reflection.

Multiple Choice

What is the formula for scale factor?

• $$\frac{new}{old}$$

• $$\frac{old}{new}$$

Multiple Choice

A ~ B. What is the scale factor of the dilation of A to B?

• $$\frac{4}{3}$$

• $$\frac{3}{4}$$

• 3

• 4

Multiple Choice

ABC ~ XYZ. What is the scale factor of the dilation of ABC to XYZ?

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

• 2

• 3