Transformation Review

Transformation Review

By Gloria [SMS]

By the end of this lesson you will be able to: 

• Generalize the properties of orientation and congruence of rotations, translations, reflections,and dilations. 

• Differentiate between transformations that preserve congruence and those that do not. 

• Explain the effect of translations, reflections over the x and y axis, and rotations limited to 90, 180, 270, and 360 as applied to 2 dimensional shapes on a coordinate plane using an algebraic representation.

• Model the effect on linear and area measurements of dilated 2 dimensional shapes.

Similar Figures

(x,y) → (1/2x, 1/2y)

Reduction, because the scale factor is less than 1.

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(x,y) → (3x,3y)

Enlargement, because the scale factor is greater than 1. 

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Does NOT Preserve congruence.

​Dilations

MULTIPLICATION

Multiple Choice

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

• (x,y) --> (0.6 - x, 0.6 - y)

• (x,y)-> (x-8, y-8)

• (x,y)-> (8/3x, 8/3y)

• (x,y) -> (0.75x, 0.75y)

Multiple Choice

A square is graphed on a coordinate plane with (x,y) representing its location. The square is transformed using the rule (x,y) -> (kx,ky). Which statement is true?

• If k is between 0 and 1, the image of the square is smaller than the square.

• If k is greater than 1, the image of the square is smaller than the square.

• If k is between 0 and 1, the image of the square is congruent to the square.

• If k is greater than 1, the image of the square is congruent to the square.

Multiple Choice

Triangle ABC was dilated with the origin as the center of dilation to create A'B'C'. Which rule was applied to triangle ABC to create figure A'B'C'?

• (x,y) -> (2x,2y)

• (x,y) -> (4x,4y)

• (x,y) -> (1/2x, 1/2y)

• (x,y) -> (1/4x, 1/4y)

Multiple Choice

Which of the following transformations does NOT preserve congruence?

• Reflections

• Rotations

• Translations

• Dilations

(x,y) → (x,-y)

Reflection over x-axis, y-coordinate changes signs.

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(x,y) → (-x,y)

Reflection over the y-axis, x-coordinate changes signs.

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Preserves congruence​

​Reflections

Multiple Choice

The coordinate grid shows figure LMN. Figure LMN will be reflected across the x-axis to create L'M'N'. Which rule describes this transformation?

• (x,y) -> (-x, y)

• (x,y) -> (-x, -y)

• (x,y) -> (x, y)

• (x,y) -> (x, -y)

Multiple Choice

Triangle LMN is reflected across the y-axis to form L'M'N'. Based on the information, which statement is true?

• The sum of the angle measures of L'M'N' is 180 more than the sum of the angle measures of triangle LMN.

• Triangle L'M'N' os congruent to triangle LMN.

• Each side length of triangle L'M'N' as 3 times the corresponding side length of triangle LMN.

• Triangle LMP and triangle L'M'N' are proportional.

Multiple Choice

Which algebraic representation of a transformation on a coordinate plane does NOT preserve congruence?

• (x,y) -> ( x+8, y+8)

• (x,y) -> (8x, -8y)

• (x,y) -> (-y, x)

• (x,y) -> (x, -y)

(x,y) → (x+4, y-3)

4 right, 3 down

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(x,y) → (x-8, y+6)

Left 8, up 6

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Preserves Congruence

Translations

Adding &

Subtracting

Multiple Choice

The coordinate grid shows a rectangle. The rectangle is translated 2 units to the left and 8 units down to create a new rectangle. Which rule describes this transformation?

• (x,y) -> (x - 2, y-8)

• (x,y) -> (x + 2, y-8)

• (x,y) -> (x - 2, y+8)

• (x,y) -> (x + 2, y+8)

Multiple Choice

Triangle PQR was transformed to create P'Q'R'. Which rule best describes the transformation?

• (x,y) -> (x-3, y-4)

• (x,y) -> (x+3, y+4)

• (x,y) -> (x+3, y-4)

• (x,y) -> (x-3, y+4)

Multiple Choice

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

• (x,y) -> (x+6, y-4)

• (x,y) -> (x-6, y-4)

• (x,y) -> (x+6, y-4)

• (x,y) -> (x-6, y+4)

90° Clockwise (CW)

1 quadrant to the right

(x,y) → (y,-x)

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90° Counterclockwise (CCW)

1 quadrant to the left

(x,y) → (-y,x)

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180° CW/CCW 

2 quadrants

(x,y) → (-x.-y)

Preserves Congruence

Rotations

Multiple Choice

The following shape is rotated 90 $$\degree$$   counterclockwise about the origin to form the new shape A'B'C'D'E'. Which rule describes this transformation?

• (x,y) -> (x, -y)

• (x,y) -> (-y, x)

• (x,y) -> (-x, y)

• (x,y) -> (y, -x)

Multiple Choice

Figure ABCDE is rotated 180 $$\degree$$  clockwise about the origin to form the figure A'B'C'D'E'. Which rule best describes this transformation?

• (x,y) -> (-x,y)

• (x,y) -> (-x,-y)

• (x,y) -> (x,-y)

• (x,y) -> (x,y)