Polygon Transformations and Congruent Figures

The pair of figures is similar. Find the missing side.

• x = 12

• x = 3

• x = 40

• x = 4

Choose the correct scale factor:

• 2

• 3

• 1/3

• 1/2

How can this transformation be represented algebraically?

• (x + 4, y)

• (-x, -y)

• (-x, y)

• (y, -x)

In a dilation what mathematical operation is used with the scale factor?

• addition 

• subtraction 

• multiplication 

• division 

A polygon will be dilated on a coordinate grid to create a larger polygon. The polygon is dilated using the origin as the center of dilation.
Which rule could represent this dilation? 

• (x,y) → (0.5 − x,0.5 − y) 

• (x,y) → (x−7,y−7) 

• (x, y) → (0.9x, 0.9y)

Triangle ABC was transformed to create triangle A′B′C′. Which rule best describes this transformation?

• (x,y)→(x,y−7)

• (x, y) → (x, −y)

• (x,y)→(x−7,y)

• (x, y) → (−x, y)

• x units

A polygon is graphed on a coordinate grid with (x, y) representing the location of a certain point on the polygon. The polygon is transformed using the rule (x, y) → (ax, ay).

Which statement must be true?

• If a is greater than 1, the image of the polygon is congruent to the polygon.

• If a is between 0 and 1, the image of the polygon is congruent to the polygon.

• If a is greater than 1, the image of the polygon is smaller than the polygon.

• If a is between 0 and 1, the image of the polygon is smaller than the polygon.

Quadrilateral PQRS was translated 5 units to the right and 3 units up to create quadrilateral P′Q′R′S′. Which rule describes this transformation?

• (x,y) → (x−5,y−3)

• (x,y) → (x+5,y+3)

• (x,y) → (x−3,y−5)

• (x,y) → (x+3,y+5)

Figure I and Figure II are similar pentagons. Which proportion must be true?

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