a The scale factor is the ratio between a length in the image and its corresponding length in the preimage.
B
b What is the scale factor of this dilation?>
C
c What is the scale factor of this dilation?
A
a 2
B
b 2.5-inch grids
C
c 2240 in.^2
Practice makes perfect
a Here is what we are told about the dimensions of the photo and drawing paper grids used to make scale drawings.
l|ccc
& Grid Size & Width & Length [0.5em] [-0.5em]
Photo& 1/4 & 5 & 7 [0.9em] [-0.5em]
Drawing paper& 1/2 & 10 & 14To find the scale factor k of the dilation, we can use either of the three dimensions. Let's focus on the corresponding lengths.
l|ccc
& Grid Size & Width & Length [0.5em] [-0.5em]
Photo& 1/4 & 5 & 7 [0.9em] [-0.5em]
Drawing paper& 1/2 & 10 & 14
The scale factor k is the ratio of the length of the photo and the length of the drawing paper. Let's write and then evaluate this quotient.
b We want to find the size of a grid that is used to make 10 times larger scale drawings. First, see that an image that is 10 times as large as the original is a dilation with a scale factor of 10.
k = 10
Now let's remember that k is the ratio of the length in the image and the corresponding length in the preimage. In this case these are the sizes of the grids.
k = image grid size/preimage grid size
Let s represent the size of the image grid. We can substitute 10 for k and 14 for the preimage grid size, and then solve for s.
c We want to find the area of a 5 * 7 grid drawing that used 2-inch grids. Here is what we know.
l|ccc
& Grid Size & Width & Length [0.5em] [-0.5em]
Photo& 1/4 & 5 & 7 [0.9em] [-0.5em]
Drawing paper& 2 & ? & ?
We will first find the scale factor of this dilation. See that the ratio of the grid size of the photo and the grid size of the drawing paper is 8. This ratio is the scale factor k.
k& =2/14
& =8
We can use this value to find the dimensions of the drawing. To do so, we multiply each dimension of the photo by k= 8.
5 * 8=40
7 * 8 =56
Now, to find the area of the grid drawing, we will multiply the resulting dimensions.
40* 56 = 2240
The area of the grid drawing equals 2240 in.^2.
