Dilations Review

In the diagram, a person who is 6 feet tall is standing on the ground 4 feet away from point P. A line segment drawn from the top corner of the building to point P creates two similar triangles. Which proportion can be used to find h, the height of the building in feet?

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

A hexagon is dilated by a factor of 2.5. Which statement correctly describes the relationship between the shape and its image?

• There is not enough information to determine the relationship.

• Both the sides and the angles are 2.5 times larger on the image.

• The side lengths stay the same, but the angles are 2.5 times larger on the image.

• The ratios of the side lengths in the original shape to their corresponding side lengths in the image are equal.

The triangle shown is dilated by a scale factor of 3 with the origin as the center of dilation. Which of the following rules represents this dilation?

• (A) (x, y) → (1/3y, 1/3x)

• (B) (x, y) → (1/3x, 1/3y)

• (C) (x, y) → (3y, 3x)

• (D) (x, y) → (3x, 3y)

Circle I was dilated with the origin as the center of dilation to create Circle II. Which rule best describes the dilation applied to Circle I to create Circle II?

• (x, y) → (3/5y, x)

• (x, y) → (3/5x, y)

• (x, y) → (3/5x, 3/5y)

• (x, y) → (x, 3/5y)

Triangle MNP graphed below is dilated with the origin as the center of dilation to create triangle M'N'P'. What is the algebraic rule for this transformation? Move the correct answer to each box. Not all answers will be used.

(x, y) → (​ (a)   ​, ​ (b)   ).

• 1/3y
• y+2
• 3y
• x+2
• 3x
• x+6
• y+6
• 1/3x

Hexagon QRSTUV shown below is dilated with the origin as the center of dilation to create hexagon Q'R'S'T'U'V'. Which of the following statements best describes this transformation?

A geometric figure is dilated by a scale factor of 3/2 with the origin as the center of dilation. What rule represents the dilation? Move the correct answer to each box. Not all answers will be used.

(x, y) → (​ ​ (a)   , ​​ (b)   )

• 2/3x
• 3/2x
• 3/2y
• 2/3y

• The area will stay the same.

Quadrilateral MRTW is dilated by a scale factor of 2/3 to create quadrilateral M'R'T'W'. The perimeter of quadrilateral MRTW is x units. What is the perimeter in units of quadrilateral M'R'T'W'?

• x units