A(1,-3) B(2,-4) A'(4,-12) B'(8,-16)
determine the scale factor used in the dilation of line segment AB, centered at the origin.
a 4
b 1/4
c -4
d 2
To determine the scale factor used in the dilation of line segment AB, centered at the origin, we need to calculate the ratio of the corresponding lengths of AB' and AB.
The length of AB' can be determined using the distance formula:
AB' = sqrt((x2-x1)^2 + (y2-y1)^2)
Using the coordinates A(1,-3) and B(2,-4) gives:
AB' = sqrt((8-1)^2 + (-16-(-3))^2)
= sqrt((7)^2 + (-13)^2)
= sqrt(49 + 169)
= sqrt(218)
The length of AB can be determined in the same way:
AB = sqrt((2-1)^2 + (-4-(-3))^2)
= sqrt((1)^2 + (-1)^2)
= sqrt(1 + 1)
= sqrt(2)
Therefore, the scale factor used in the dilation is AB'/AB:
scale factor = AB'/AB
= sqrt(218)/sqrt(2)
= sqrt(109)
From the given options, the scale factor is not 4, 1/4, -4, or 2.