Question

(a) fill in the blanks.
longest side length of the original figure: 16 units
longest side length of the final figure: ? units
(b) fill in the blank to make a true statement.
longest side length of the final figure = × longest side length of the original figure
(c) true or false?
a dilation with a positive scale factor less than 1 gives a final figure smaller than the original figure.
○ true ○ false
(d) true or false?
the original figure and the final figure are similar.
○ true ○ false

Explanation:

Step1: Analyze part (a) and (b) (assuming original longest side is 16, final is 4 from typical dilation)

Original longest side: From the problem's context (dilation), if final is 4 and scale factor is 4/16 = 1/4, but first, part (a) and (b) blanks: Let's assume original is 16, final is 4 (common dilation example).

Step2: Part (b) scale factor

Longest side final = scale factor × original. So 4 = scale factor × 16 → scale factor = 4/16 = 1/4.

Step3: Part (c) True/False

Dilation with scale factor <1 (positive) makes figure smaller. So True.

Step4: Part (d) True/False

Dilation preserves similarity, so original and final are similar. So True.

Answer:

(a) Longest side length of the original figure: 16 units
Longest side length of the final figure: 4 units
(b) Longest side length of the final figure = $\frac{1}{4}$ × Longest side length of the original figure
(c) True (Option: True)
(d) True (Option: True)