The endpoints of AB are A (8,4) and B(6,-2). The endpoints of its image after a dilation are A' (5,2.5) and B'(3.75,-1.25). Find the scale factor. Please enter your scale factor as a whole number or a fraction. No Decimals(3 points)
To find the scale factor, we can use the formula:
scale factor = image length / original length
First, we need to find the lengths of AB and A'B'.
Length of AB:
AB = sqrt((6-8)^2 + (-2-4)^2)
AB = sqrt((-2)^2 + (-6)^2)
AB = sqrt(40)
AB = 2sqrt(10)
Length of A'B':
A'B' = sqrt((3.75-5)^2 + (-1.25-2.5)^2)
A'B' = sqrt((-1.25)^2 + (-3.75)^2)
A'B' = sqrt(5.625 + 14.0625)
A'B' = sqrt(19.6875)
A'B' = sqrt(125/4)
A'B' = 5/2 sqrt(5)
Now we can find the scale factor:
scale factor = A'B' / AB
scale factor = (5/2 sqrt(5)) / (2 sqrt(10))
scale factor = 5/4 sqrt(5)/sqrt(10)
scale factor = 5/4 sqrt(5)/2
scale factor = 5/8 sqrt(5)
Therefore, the scale factor is 5/8.