Use the lengths of corresponding sides to calculate the scale factor of the dilation.
1 foot
Practice makes perfect
We see that the projection of the rectangle ABCD is a dilation with center O. Using the ratio between the corresponding sides, we can find its scale factor n.
We see that AB= 3 inches and A'B'= 1 foot. Before finding n, we need to convert between inches and feet. Multiplying 3 inches by the conversion factor of 1 foot12 inches will convert it to feet.
3 inches * 1 foot/12 inches =1/4 feet
We are ready to find the scale factor n.
n=A'B'/AB= 1/14= 4
Finally, we can find the distance from each vertex of ABCD to the light, or to the point O. By the properties of dilations we know that the ratio of OB' to OB is the same as the scale factor, 4. We are given that the length of BB' is 3 feet. Let's review the diagram again.
We want to compare the length of OB' to the length of OB. After substituting the length of BB' and the scale factor to find the formula for the scale factor, we have the equation below.
n=OB'/OB ⇒ 4=x+3/x
Let's solve for x.
