Scale Factor, Dilation
What are the two components of a dilation?
A center and scale factor
2/3
A child's picnic table is a scale model of an adult picnic table. The child's picnic table is 22 inches tall, and the adult picnic table is 33 inches tall. What is the model's scale factor?
80
A museum of natural history is making a scale model of a carpenter ant. The scale used is 12.5cm:1mm. If the actual length of the ant is 6.4 mm, what is the length of the model?
20
A picture of a cake has a measurement of 8 inches across. Using a scale factor of 1: 2.5, how many inches across is the actual cake? (enter just the number, not the unit name)
108
A rectangular rabbit coop has a base with a length of 6 feet and a width of 2 feet. We are using a scale factor of 3:1 to build a new base for our growing rabbit family. What is the area of the new base?
1.25
A statue of Euclid's face has a scale factor of ¼ when comparing it to a picture of his face. If the statue of Euclid's face measures 5 inches across, then how many inches across is the picture? (enter as a decimal; do not enter the unit name)
48
A tree branch, compared to its picture, has a scale factor of 1/16. If the picture measures 3 inches across, how long is the actual tree branch? (do not enter the unit name)
315
A triangle has three 60 degree angles and three sides of length 60 cm. The triangle is dilated (made larger) with a scale factor of 1.75. What is the perimeter of the image?
Point A (20, 10) was dilated by a scale factor of 1/2. What are the coordinates of A'?
A' (10, 5)
Point A (2,3), Point B (1, -4), and Point C (1, 1) were dilated by a scale factor of 2. What are the coordinates of A', B', C'?
A'(4,6) B'(2, -8) C'(2, 2)
A(4 , 5) B (1, 2) C( 1, 3), D (9, 6). r=12
A'(48, 60) B'(12, 24) C'(12, 36) D'(108, 72)
When is a time in real-life that dilation are used?
Ads, building models (blue prints), etc...
1:6
An artist is making a scaled drawing of a 4 ft. wide mural. The drawing is 8 inches wide. What is the drawing's scale?
How do you find scale factor?
Divide the image length by the original length
Does a dilation of 5/3 shrink or enlarge a figure?
Enlarge
5
If a map's scale is 1:5 then the scale factor from the map to the original scale is ?
1:12
If a map's scale is 3:36 then the scale factor from the map to the original scale is ?
12
If side AB was enlarged by a scale factor of 4. What would its new length be? (enter just the number, not the unit name)
How do you find coordinates after a dilation?
Multiply the original coordinates by the scale factor.
Will negative coordinates be positive after a dilation?
No because scale factor is always positive and a negative multiplied with a positive number is negative.
48
On a map, two sites are 2 in apart. The scale factor is 1 in. : 24 mi. What is the actual distance?
What is preserved in dilations?
Shape
4.5
The Museum of Science and Industry in Chicago has a scale model of a human heart that is large enough for people to walk through. The height of the scale model is 16 ft. The scale used is 1 ft : 9/32 in. What is the height of the actual heart on which the model is designed?
4.6
The liquid core of Earth is 2300 km thick. A scale model of the layers of the Earth has a scale of 1 in:500 km. How thick is the liquid outer core of the model?
9
The picture of a car has a scale of 1 inch to 3 feet. If the picture measures 3 inches across, then how many feet long is the actual car?
10
The scale of a model airplane is 1 in : 3.5 ft. The wingspan of the plane is 35 ft. What is the wingspan of the model?
3.4
There is a scale model of the White House in Tobu World Square in Japan. The scale used for the model is 1:25. The height of the main building of the White House is 85 feet. Find this height on the model.
B is a triangle. After a dilation of 1/2, what is the shape of B'?
Triangle
If a figure is getting larger the scale factor is ________. If a figure is getting smaller the scale factor is ________.
greater than 1, r>1 Less than 1, but greater than 0, 0
A(12, 6) A' (2, 1) What is the scale factor?
r=1/6
What is the scale factor that would map line segment AB ,9 cm, to line segment A'B' ,18 cm?
r=2
A(3, 6) A' (9, 18) What is the scale factor?
r=3