Scale Factors and Similarity

a)  If a scale factor of ½ is applied, what would be the algebraic representation for this dilation.

• (x, y)--> (2x, 2y)
• (x, y)--> (1/2x, 1/2y)
• (x, y)--> (x+2, y+2)
• (x, y)--> (x-2, y-2)

Triangle ABC is dilated with a scale factor of 1/2.  What is the ordered pair for C’?

• C’ (2 , 1)
• C’ (-2 , 1)
• C’ (2 , -1)
• C’ (-2 , -1)

Triangle ABC was dilated to create triangle A’B’C’.  The table below shows to coordinates of the original triangle and its dilation.
Which algebraic rule represents the dilation?

• (x, y)--> (3x, 3y) 
• (x, y)--> (6x, 10y)
• (x, y)--> (2x, 2y)
• (x, y)--> (1/2x,  1/2y)

The best description of a dilation of a figure is ____________________________.

• a mirror image of the figure
• an enlargement or a reduction of the figure
• the turning of the figure about some fixed point
• a slide of the figure

Classify the dilation as an enlargement or reduction.

• enlargement
• reduction

What is the scale factor?

• 4/7
• 7/4
• 5/3
• 2/5

9  Rectangle ABCD has vertices A (−1, 2), B (4, 2), C (4, −1), and D (−1, −1). Rectangle ABCD is dilated by a scale factor of 3/4  . Which statement is true?

• Rectangle ABCD and rectangle A′B′C′D′ are congruent.
• Rectangle ABCD and rectangle A′B′C′D′ are similar. Rectangle ABCD is larger than rectangle A′B′C′D′.
• Rectangle ABCD and rectangle A′B′C′D′ are similar. Rectangle ABCD is smaller than rectangle A′B′C′D′.
• Rectangle ABCD and rectangle A′B′C′D′ are similar. Rectangle ABCD is the same size as rectangle A′B′C′D′.

A triangle has a side length of 4 inches and an area of 18 square inches and a larger similar triangle has a corresponding side length of 8 inches. What scale factor was used to dilate the smaller triangle to the larger one?

• A    Enlargement by a scale factor of 18
• A    Reduction by a scale factor of .25
• A    Reduction by a scale factor of 1/2
• A    Enlargement by a scale factor of 2

Which of the following are attributes of similar figures.  
I  Angles are proportional
II  Sides are proportional  
III Angles are congruent  
IV Sides are congruent

• I and II only
• II and III only
• III only
• III and IV

Use the diagram to the right to determine the distance across  Catfish Lake. Assume the triangles are similar. 

• 6.75 km
• 4.1 km
• 2 km
• 3 km