Dilations Sampler

A triangle with a vertex at point Y (-3, 7) is dilated by a scale factor represented by the coordinate pair ( $\frac{2}{3}$  x, $\frac{2}{3}$  y). What is the location of Y’? (Hint: create a table)

• Y’ (-2, 4 $\frac{2}{3}$ )

• Y’ (-2, 4)

• Y’ (-3 $\frac{2}{3}$ , 7 $\frac{2}{3}$ )

• Y’ (-6, 14)

A triangle with vertices E (-9, 6), F (-6, -5), and G (4, 0) is dilated to form a triangle with vertices E’(-3, 2), F’(-2, -1), and G’ (1, 0). Write an algebraic expression that explains the effect of the scale factor applied to triangle EFG to form triangle E’F’G’ .

• (x, y) $\rightarrow$ ( $\frac{1}{3}$ x, $\frac{1}{3}$ y)

• (x, y) $\rightarrow$ (3x, 3y)

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

• (x, y) $\rightarrow$ (-3x, -3y)

Triangle XYZ is dilated to form triangle X’Y’Z’.

Which shows the scale factor used to dilate triangle XYZ to form triangle X’Y’Z’?

• (3x, 3y)

• (2x, 2y)

• 
  

  ( $\frac{1}{2}$ x, $\frac{1}{2}$ y)

• ( $\frac{1}{3}$ x, $\frac{1}{3}$ y)

ΔABC is dilated using a scale factor of 2. What happens to its angle measures?

• They double in size.

• They do not change.

• It depends on the center of the dilation.

• They become half as great.

ΔABC is dilated using a scale factor of 2.5. Which property does not change?

• perimeter

• area

• angle measures

• side lengths

If a scale factor is greater than one, then the figure gets

• smaller

• bigger

• disappears

• negative

If a scale factor is less than one, then the figure gets

• bigger

• smaller

• negative

• disappears

Point R is located at (-2, -3). Point R' is located at (-6, -9). What is the scale factor?

• 
  

  ( $\frac{1}{3}$ x, $\frac{1}{3}$ y)
  

• (3x, 3y)

• ( $\frac{2}{3}$ x, $\frac{6}{9}$ y)

• (1.5x, 1.5y)

A polygon will be dilated to create a larger polygon. The origin will be the center of dilation. Which rule COULD represent this dilation?

• (x,y) $\rightarrow$ (0.5 - x, 0.5 - y)
  

• (x,y) $\rightarrow$ (x - 7, y - 7)

• (x,y) $\rightarrow$ ( $\frac{5}{4}$ x, $\frac{5}{4}$ y)

• (x,y) $\rightarrow$ (0.9x, 0.9y)

A figure is graphed on a coordinate grid with (x,y) representing the location of a certain point of the figure. The figure is transformed using the rule (x,y)

 $\rightarrow$  (kx, ky).  Which statement must be true?

• If k is greater than 1, the image will be congruent.

• If k is between 0 and 1, the image will be congruent.

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

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