Transformations Review A2 Edition

Multiple Choice

Triangle JVA is dilated with the origin as the center of dilation to create triangle J'V'A'. Which rule best represents the dilation that has been applied to triangle JVA to create triangle J'V'A'?

• (x, y) → (x - 3, y - 3)

• (x, y) → (x - 4, y - 4)

• (x, y) → (1/4x, 1/4y)

• (x, y) → (4x, 4y)

Multiple Choice

Pentagon PENTA is shown on a coordinate grid. Pentagon PENTA is dilated with the origin as the center of dilation using the rule (x, y) → (5/4x, 5/4y) to create pentagon P'E'N'T'A'. Which statement is true?

• Pentagon P'E'N'T'A' is larger than pentagon PENTA, because the scale factor is greater than 1.

• Pentagon P'E'N'T'A' is smaller than pentagon PENTA, because the scale factor is less than 1.

• Pentagon P'E'N'T'A' is smaller than pentagon PENTA, because the scale factor is greater than 1.

• Pentagon P'E'N'T'A' is larger than pentagon PENTA, because the scale factor is less than 1.

Multiple Choice

Quadrilateral PQRS is dilated with the origin as the center of dilation to create triangle P'Q'R'S'. Which rule best represents the dilation that has been applied to triangle PQRS to create triangle P'Q'R'S'?

• (x, y) → (x + 2, y + 1)

• (x, y) → (x − 2, y + 4)

• (x, y) → (0.5x, 0.5y)

• (x, y) → (2x, 2y)

Other Transformations

Translations - moving a shape left, right, up, or down.
Reflections - Flipping a shape over a line of reflection like the x or y axis.
Rotations - Turning a shape either clockwise or counterclockwise.

Important

Congruenence and Orientation

Congruence - The shape stays the same size. Only dilations doesn't preserve congruence.

Orientation - The angles of the shapes change directions. Only reflections change orientation.
Remember Dilations change congruence. Orientation changes Reflections.

Multiple Choice

Trapezoid DEFG is rotated 180° about the origin to form trapezoid D'E'F'G'. Which statement is true?

• The sum of the angle measures of trapezoid DEFG is 180° less than the sum of the angle measures of trapezoid D'E'F'G'.

• Trapezoid DEFG is not congruent to trapezoid D'E'F'G'.

• The area of trapezoid DEFG is less than the area of trapezoid D'E'F'G'.

• The angle measures of trapezoid DEFG are equal to the corresponding angle measures of trapezoid D'E'F'G'.

Multiple Choice

Rectangle ABCD is transformed according to the rule (x, y) → (x + 3, y - 6). Which statement is true?

• The angle measures of rectangle A'B'C'D' are greater than the corresponding angle measures of rectangle ABCD.

• The angle measures of rectangle A'B'C'D' are equal to the corresponding angle measures of rectangle ABCD.

• The side lengths of rectangle A'B'C'D' are 3 units longer than the corresponding side lengths of rectangle ABCD.

• The side lengths of rectangle A'B'C'D' are 6 units shorter than the side lengths of rectangle ABCD.

Multiple Choice

Which representation of a transformation on a coordinate grid does not preserve congruence?

• (x, y) → (x + 5, y + 5)

• (x, y) → (−x, −y)

• (x, y) → (−y, x)

• (x, y) → (0.2x, 0.2y)

Multiple Choice

A transformation was applied to a figure to create a new figure. Which transformation does not preserve congruence?

• A rotation of 180°

• A dilation by a scale factor of 3

• A translation 4 units up

• A reflection across the y-axis

Multiple Choice

Quadrilateral DEFG is shown on the coordinate grid. A student reflected the quadrilateral DEFG across the y-axis to create quadrilateral DE'F'G'. Which rule describes this transformation? [diagram]

• (x, y) → (−x, −y)

• (x, y) → (−x, y)

• (x, y) → (−y, x)

• (x, y) → (x + 3, y − 3)

Multiple Choice

Triangle ABC was translated 5 units to the left and 3 units up to create triangle A'B'C'. Which rule best describes this transformation?

• (x,y) → (5x, −3y)

• (x,y) → (−5x, 3y)

• (x,y) → (x − 5, y + 3)

• (x,y) → (x + 5, y + 3)

Multiple Choice

Triangle ABC was translated 5 units down and 2 units to the right to create triangle A'B'C'. Which rule best describes this transformation?

• (x, y) → (x − 5, y + 2)

• (x, y) → (x + 2, y − 5)

• (x, y) → (x + 5, x − 2)

• (x, y) → (x − 2, y + 5)

Multiple Choice

A figure is graphed on a coordinate grid and then rotated 90° counterclockwise. If the center of the original figure was located at (x, y), which ordered pair represents the center of the new figure after the transformation?

• (x, y)

• (−x, y)

• (−y, x)

• (y, −x)

Multiple Choice

The coordinate grid shows pentagon PENTA. Pentagon PENTA is reflected over the x-axis to create pentagon P'E'N'T'A'. Which rule describes this transformation?

• (x, y) → (−x, −y)

• (x, y) → (−y, x)

• (x, y) → (−x, y)

• (x, y) → (x, −y)

Multiple Choice

The coordinates of the vertices of a triangle are A(2, 1), B(3, 5), C(7, 0). Triangle ABC is reflected across the x-axis to create triangle A'B'C'. Which rule describes this transformation?

• (x, y) → (−x, y)

• (x, y) → (x, −y)

• (x, y) → (−y, x)

• (x, y) → (y, −x)

Multiple Choice

Quadrilateral RSTU was translated 5 units to the left. Which rule describes the translation that was applied to triangle RSTU to create R'S'T'U'?

• (x, y) → (−5x, y)

• (x, y) → (x − 5, y)

• (x, y) → (x, −5y)

• (x, y) → (x, y − 5)

Multiple Choice

A square with a perimeter of 10 units is graphed on a coordinate grid. The square is dilated by a scale factor of 3 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?

• (x + 10, y + 10)

• (10x, 10y)

• (3x, 3y)

• (x + 3, y + 3)

Multiple Choice

Quadrilateral DEFG is shown on the coordinate grid. A student rotated the quadrilateral DEFG 180° to create quadrilateral DEFG. Which rule describes this transformation?

• A. (x, y) → (−x, −y)

• B. (x, y) → (−x, y)

• C. (x, y) → (−y, x)

• D. (x, y) → (x + 3, y − 3)

Multiple Choice

Triangle ABC was reflected over the y-axis to create triangle A'B'C'. Which rule best describes this transformation?

• (x, y) → (x, y)

• (x, y) → (−x, −y)

• (x, y) → (−y, x)

• (x, y) → (−x, y)

Multiple Choice

Quadrilateral RSTU was translated 3 units to the right and 2 units down. Which rule describes the translation that was applied to triangle RSTU to create R'S'T'U'?

• (x, y) → (3x, -2y)

• (x, y) → (-2x, 3y)

• (x, y) → (x + 3, y - 2)

• (x, y) → (x - 2, y + 3)

Got that?

The perimeter of the shape will increase or decrease by a factor that is the SAME of the scale factor.
Area will increase or decrease by a factor of scale factor squared.

Multiple Choice

A rectangle has a perimeter of 15 inches. The image is created with a scale factor of 2. What is the new perimeter?

• 120
• 7.5
• 30
• 15

Multiple Choice

A rectangle has a area of 10cm². The image is created with a length scale factor of 4. What is the new area?

• 160
• 40
• 400
• 16

Multiple Choice

If the linear scale factor is 5, what is the area scale factor?

• 15
• 125
• 25
• 5

Multiple Choice

A scale factor of 2 is used to enlarge the dimensions of a square. What is the effect of this change on the area of the square?

• The area will be half as big.

• The area will be twice as large.

• The area will be 4 times larger.

• The area will be 8 times larger.

• The area will not change.

Multiple Choice

A figure is dilated by a scale factor of $$\frac{1}{4}$$ . How will the perimeter of the figure be effected?

• It will be $$\frac{1}{4}$$ as larger as the original.

• It will be $$4$$ times larger as the original.

• It will be 8 times larger as the original.

• It will be $$\frac{1}{16}$$ as larger as the original.