Question

for the figure, do a dilation centered at the origin with a scale factor of \\(\frac{1}{4}\\). then answer each part.

(a) fill in the blanks.
longest side length of the original figure: \\(\square\\) units
longest side length of the final figure: \\(\square\\) units
(b) fill in the blank to make a true statement.

Explanation:

Step1: Find original longest side

The original figure is a trapezoid. The longest side (the base) spans from \( x = 2 \) to \( x = 18 \) (assuming the left - most point of the base is at \( x = 2 \) and the right - most at \( x = 18 \)). The length is \( 18 - 2=16 \) units.

Step2: Find length after dilation

The scale factor of dilation is \( \frac{1}{4} \). To find the length of the longest side of the final figure, we multiply the original length by the scale factor. So, the length is \( 16\times\frac{1}{4} = 4 \) units.

Answer:

Longest side length of the original figure: \( 16 \) units
Longest side length of the final figure: \( 4 \) units