Question

if a dilation is centered at (2, 2) with a scale factor of 3, what is the coordinate of (4, 6) after dilation?
a. (7, 10)
b. (6, 9)
c. (8, 14)
d. (5, 8)

an architect designs a skyscraper that is 100 meters wide. if the scale factor for the model is 0.05, what is the width of the model?
a. 3 meters
b. 6 meters
c. 5 meters
d. 4 meters

what is the result of a dilation with a scale factor between 0 and 1?
a. the figure stays the same size
b. the figure is reduced in size
c. the figure enlarges
d. the figure disappears

an architect designs a skyscraper that is 200 meters tall. if the scale factor for the model is 0.05, what is the height of the model?
a. 8 meters
b. 5 meters
c. 10 meters
d. 12 meters

Explanation:

Step1: Dilation formula

The formula for dilation centered at \((h,k)\) with scale factor \(s\) is \((x',y')=(h + s(x - h),k + s(y - k))\). Here \(h = 2,k = 2,s = 3,x = 4,y = 6\).

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Step2: Scale - model relationship

For the model - skyscraper relationship, if the actual size is \(A\) and the scale factor is \(s\), the model size \(M=A\times s\).
For the first model (width): \(A = 100\) meters, \(s=0.05\), then \(M = 100\times0.05=5\) meters.
For the second model (height): \(A = 200\) meters, \(s = 0.05\), then \(M=200\times0.05 = 10\) meters.

Step3: Dilation scale - factor property

If the scale factor \(0\lt s\lt1\) in a dilation, the figure is reduced.

Answer:

1. c. \((8,14)\)
2. c. \(5\) meters
3. b. The figure is reduced in size
4. c. \(10\) meters