Question

1. an engineer designs a model bridge that is 1/50th the size of the actual bridge. if the actual bridge is 1000 meters long, what is the length of the model?

a. 35 meters
b. 30 meters
c. 20 meters
d. 25 meters

1. what remains unchanged in a figure after a dilation?

a. the area of the figure
b. the position of the figure
c. the size of the figure
d. the shape and angles measures of the figure

1. two circles have diameters of 8 and 24, and their centers are 5 units apart. what transformations are needed to map the smaller circle onto the larger circle?

a. translation and reflection
b. rotation and dilation
c. reflection and dilation
d. dilation and translation

Explanation:

Question 13

Step1: Identify the scale factor and actual length

The scale factor is $\frac{1}{50}$ and the actual length is 1000 meters.

Step2: Calculate the model length

To find the model length, multiply the actual length by the scale factor: $1000\times\frac{1}{50}$
$1000\div50 = 20$

Dilation is a transformation that changes the size of a figure (scaling it up or down) but preserves the shape and angle measures. The area changes (scales by the square of the scale factor), the position isn't necessarily preserved (though center of dilation affects, but size changes, area changes, position can change, but shape and angles remain).

First, the smaller circle has diameter 8, larger has 24. The scale factor for dilation is $\frac{24}{8}=3$, so dilation is needed to make the smaller circle the same size as the larger. Then, since their centers are 5 units apart, we need to translate (move) the smaller circle (after dilation) to the center of the larger circle. Rotation and reflection aren't needed here as circles are symmetric. So dilation (to scale) and translation (to move) are required.

Answer:

c. 20 meters

Question 14