Quiz about Transformations

Question 1

Triangle TRW is shown on the coordinate grid. Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair represents the location of point R' ?

Accepted Answer

$$\left(-3n,\ -5n\right)$$

Answer

$$\left(-\frac{3}{n},-\frac{5}{n}\right)$$

Answer

$$\left(-3+n,\ -5+n\right)$$

Answer

$$\left(-3-n,\ -5-n\right)$$

Answer

$$\left(-5n,\ -3n\right)$$

Question 2

Triangle XYZ is rotated $$90\degree$$ clockwise about the origin to form triangle X'Y'Z'.

Which statement is true?

Accepted Answer

The area of triangle XYZ is equal to the area of triangle X'Y'Z'.

Answer

The sum of the angle measures of the triangle XYZ is $$90\degree$$ less than the sum of the angle measures of triangle X'Y'Z'.

Answer

The angle measures of triangle XYZ are less than the corresponding angle measures of triangle X'Y'Z'.

Answer

Triangle XYZ is not congruent to triangle X'Y'Z'.

Question 3

A transformation is applied to a figure to create a new figure on a coordinate grid. Which transformation does not preserve congruency?

Accepted Answer

A dilation by a scale factor of 0.75

Answer

A rotation of $$270\degree$$ clockwise

Answer

A reflection across the x-axis

Answer

A translation of 2 units down and 4 units right

Question 4

The vertex Q' will be located at (21, 7). Fill in the information missing from the rule below that would be for this dilation.

$$\left(x,y\right)\rightarrow$$ ________

Accepted Answer

$$\left(\frac{7}{2}x,\frac{7}{2}y\right)$$

Answer

$$\left(\frac{2}{7}x,\frac{2}{7}y\right)$$

Answer

$$\left(-\frac{7}{2}x,-\frac{7}{2}y\right)$$

Answer

$$\left(x-15,\ y+5\right)$$

Answer

$$\left(-\frac{2}{7}x,\ -\frac{2}{7}y\right)$$

Question 5

Which statements is true?

Accepted Answer

The angle measures of P'R'S'T' are equal to the corresponding angle measures of PRST.

Accepted Answer

Side lengths of P'R'S'T' are congruent to corresponding side lengths of PRST.

Answer

The side lengths of P'R'S'T' are twice the corresponding side lengths of P'R'S'T'.

Answer

The side lengths of P'R'S'T' are 9 units longer than the corresponding side lengths of PRST.

Answer

The angle measures of P'R'S'T' are greater than the corresponding angles of PRST.

Question 6

Which representation of a transformation on a coordinate grid preserves congruency?

Accepted Answer

$$\left(x,\ y\right)\rightarrow\left(x,\ y-5\right)$$

Accepted Answer

$$\left(x,\ y\right)\rightarrow\left(-x,\ y\right)$$

Accepted Answer

$$\left(x,\ y\right)\rightarrow\left(-y,\ x\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(\frac{2}{3}x,\ \frac{2}{3}y\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(4x,\ 4y\right)$$

Question 7

Triangle HJK is graphed on the coordinate grid. Triangle HJK will be transformed using the rule $$\left(x,\ y\right)\rightarrow\left(-x,\ y\right)$$ to create triangle H'J'K'. Which graph represents triangle H'J'K' ?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 8

A circle is graphed on a coordinate grid with its center at (5, -4). The circle will be translated c units down and b units to the left. Which rule describes the center of the new circle after the translation.

Accepted Answer

$$\left(x,\ y\right)\rightarrow\left(5-b,-4-c\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(5-c,\ -4-b\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(5+b,-4+c\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(b-5,\ c-4\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(-5+c,-4-b\right)$$

Question 9

A figure was transformed on a coordinate grid using the rule $$\left(x,\ y\right)\rightarrow\left(x,\ -y\right).$$ Which of the following describes the transformation?

Accepted Answer

A reflection across the x-axis

Answer

A $$180\degree$$ rotation counterclockwise

Answer

A $$90\degree$$ rotation counterclockwise

Answer

A reflection across the y-axis

Answer

A translation down 1 unit

Question 10

The pentagon is reflected across the x-axis to create V'W'X'Y'Z'. Which rule describes this transformation?

Accepted Answer

$$\left(x,\ y\right)\rightarrow\left(x,\ -y\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(-x,\ y\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(-x,-y\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(-y,\ x\right)$$

Answer

$$\left(x,\ y\right)\rightarrow\left(y,\ -x\right)$$

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