Question

1. a line segment is dilated with a scale factor ( k = 4 ). if the original length of the segment is 5, what is the length of the image?

a. 20
b. 15
c. 25
d. 10

1. what is the result of dilating a rectangle by a scale factor of ( k = 1 )?

a. the figure remains the same.
b. the figure changes shape.
c. the figure enlarges.
d. the figure reduces.

1. a city planner created a scaled map of a residential area. the actual area is defined by having a length of 800 meters and width of 500 meters. using a scale factor of 0.02, what is the width of the scaled map?

a. 5 meters
b. 8 meters
c. 10 meters
d. 12 meters

Explanation:

Question 7

Step1: Recall dilation formula

The length of a dilated segment is original length times scale factor, i.e., \( \text{Image Length} = \text{Original Length} \times k \)

Step2: Substitute values

Original length = 5, \( k = 4 \), so \( \text{Image Length} = 5 \times 4 = 20 \)

Dilation with scale factor \( k = 1 \) means each coordinate (or length) is multiplied by 1, so the figure's size and shape remain unchanged. Option a is correct as dilation preserves shape, and \( k = 1 \) doesn't change size.

Step1: Recall dilation for length

Scaled width = actual width × scale factor

Step2: Substitute values

Actual width = 500 meters, scale factor = 0.02, so \( \text{Scaled Width} = 500 \times 0.02 = 10 \) meters

Answer:

a. 20

Question 8