Question

rectangle r with side lengths 4 and 6 is dilated by a scale factor of 2. what are the side lengths of the resulting rectangle?
○ a. 10 and 15
○ b. 2 and 3
○ c. 8 and 12
○ d. 6 and 9

which transformation involves sliding a figure from one place to another without changing its shape or size?
○ a. rotation
○ b. dilation
○ c. reflection
○ d. translation

a trapezoid has vertices a(-3, -1), b(-1, -1), c(-2, -3), and d(-4, -3). after translation, the new vertices are a(0, 2), b(2, 2), c(1, 0), and d(-1, 0). what is the translation rule?
○ a. (x - 3, y - 3)
○ b. (x + 3, y + 3)
○ c. (x - 1, y - 2)
○ d. (x + 3, y - 3)

Explanation:

First Question:

Step1: Recall dilation rule

Dilation multiplies side lengths by the scale factor.

Step2: Calculate new side lengths

Original sides: 4 and 6. Scale factor = 2.
New side 1: \( 4 \times 2 = 8 \)
New side 2: \( 6 \times 2 = 12 \)

• Rotation: Turns the figure.
• Dilation: Changes size.
• Reflection: Flips the figure.
• Translation: Slides the figure (shape/size unchanged).

Step1: Analyze x - coordinate change

For point \( A(-3, -1) \to A'(0, 2) \):
\( -3 + 3 = 0 \) (x - change: +3).

Step2: Analyze y - coordinate change

\( -1 + 3 = 2 \) (y - change: +3).
Check other points (e.g., \( B(-1, -1) \to B'(2, 2) \): \( -1 + 3 = 2 \), \( -1 + 3 = 2 \)) to confirm.

Answer:

c. 8 and 12

Second Question: