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
To find the scale factor, we can use the distance formula.
The length of segment AB is given by:
AB = sqrt((6-8)^2 + (-2-4)^2) = sqrt((-2)^2 + (-6)^2) = sqrt(4 + 36) = sqrt(40) = 2sqrt(10)
The length of segment A'B' is given by:
A'B' = sqrt((3.75-5)^2 + (-1.25-2.5)^2) = sqrt((-1.25)^2 + (-3.75)^2) = sqrt(1.5625 + 14.0625) = sqrt(15.625) = 3.75
The scale factor is the ratio of the lengths of the segments:
Scale factor = A'B' / AB = 3.75 / 2sqrt(10) = 3.75 / (2*sqrt(10)) = 3.75 / (2*sqrt(10)) * (sqrt(10)/sqrt(10)) = (3.75*sqrt(10)) / 20 = 3(sqrt(10)) / 20
So, the scale factor is 3/20.