Dilations on a Grid

On graph paper, sketch the image of quadrilateral PQRS under the dilation centered at \(S\) with scale factor \(\frac{1}{2}\).

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Triangle (ABC) is dilated using (D) as the center of dilation with scale factor 2. The image is triangle (A'B'C'). Clare says the two triangles are congruent, because their angle measures are the same. Do you agree? Explain how you know.

• Yes

• No

How do you write the algebraic notation when the scale factor is 1/2?

• (x, y) goes to (2x, 2y)

• (x, y) goes to (1/2x, 1/2y)

• (x, y) goes to (-2x, -2y)

• (x, y) goes to (2x, 1/2y)

The __________ is the ratio of a length of the new figure to the corresponding length on the original figure.

• reduction

• enlargement

• scale factor

• center of dilation

Choose the correct scale factor:

• 2.5

• 1.5

• 3.5

• 4

What is the scale factor if the triangle on the left is the original?

• 2

• 3/2

• 2/3

• 1/2

What is the scale factor used to dilate the small square to the larger square given there areas?

• 4

• 16

• 3

• 12

What is the scale factor used to dilate the small square to the larger square given there perimeters?

• 3

• 4

• 12

• 1/3

A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation. If (x,y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

• (20x, 20y)

• (0.4x, 0.4y)

• (x + 20, y + 20)

• (x + 0.4, y + 0.4)

Triangle MNP is graphed on a coordinate grid with vertices at M(-3, -6), N(0, 3) and P(6, -3). Triangle MNP is dilated by a scale factor of u with the origin as the center of dilation to created triangle M'N'P'. Which ordered pair represents the coordinates of vertex P'?

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