Question

what is the formula for dilating a point when the center of dilation is at the origin?
○ a. (x,y) → (k + x,k + y)
○ b. (x,y) → (kx,ky)
○ c. (x,y) → (x^k,y^k)
○ d. (x,y) → (x/k,y/k)

a model of a new building is created using a scale factor of 0.1. if the actual building is 150 meters tall, what is the height of the model?
○ a. 5 meters
○ b. 20 meters
○ c. 15 meters
○ d. 10 meters

a bridge is 100 meters wide and is being scaled down by a factor of 0.02 for a model. what is the width of the model of the bridge?
○ a. 5 meters
○ b. 4 meters
○ c. 6 meters
○ d. 7 meters

an urban planner is creating a model of a city block that is 600 meters long. using a scale factor of 0.02, what is the length of the scaled - down model?
○ a. 14 meters
○ b. 16 meters
○ c. 12 meters
○ d. 10 meters

a bridge is 1200 meters long and is being scaled down by a factor of 0.02 for a model. what will be the length of the model bridge?
○ a. 20 meters
○ b. 24 meters
○ c. 12 meters
○ d. 15 meters

a model of a sports arena is being created using a scale factor of 0.04. if the actual arena is 500 meters wide, what is the width of the model?
○ a. 35 meters
○ b. 20 meters
○ c. 30 meters
○ d. 25 meters

Explanation:

Step1: Dilating a point at origin

When dilating a point \((x,y)\) with center at the origin and scale factor \(k\), the formula is \((x,y)\to(kx,ky)\). So for the first question, option b is correct.

Step2: Model height calculation

For the model of building with scale factor \(0.1\) and actual height \(150\) meters. Using the formula \(h_{model}=h_{actual}\times scale - factor\), we have \(h_{model}=150\times0.1 = 15\) meters. So for the second question, option c is correct.

Step3: Bridge width calculation

For the bridge with actual width \(100\) meters and scale factor \(0.04\). Using \(w_{model}=w_{actual}\times scale - factor\), we get \(w_{model}=100\times0.04=4\) meters. So for the third question, option b is correct.

Step4: City - block length calculation

For the city - block with actual length \(600\) meters and scale factor \(0.02\). Using \(l_{model}=l_{actual}\times scale - factor\), we have \(l_{model}=600\times0.02 = 12\) meters. So for the fourth question, option c is correct.

Step5: Bridge length calculation

For the bridge with actual length \(1200\) meters and scale factor \(0.02\). Using \(l_{model}=l_{actual}\times scale - factor\), we get \(l_{model}=1200\times0.02=24\) meters. So for the fifth question, option b is correct.

Step6: Arena width calculation

For the arena with actual width \(500\) meters and scale factor \(0.04\). Using \(w_{model}=w_{actual}\times scale - factor\), we have \(w_{model}=500\times0.04 = 20\) meters. So for the sixth question, option b is correct.

Answer:

1. b \((x,y)\to(kx,ky)\)
2. c \(15\) meters
3. b \(4\) meters
4. c \(12\) meters
5. b \(24\) meters
6. b \(20\) meters