3. Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin. A' (-6,8) B' (4,-8) and A (-3,4) B (2,-4)
To find the scale factor used in the dilation, we can compare the lengths of corresponding line segments.
The length of line segment AB is calculated using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
AB = √[(2 - (-3))^2 + (-4 - 4)^2]
AB = √[5^2 + (-8)^2]
AB = √[25 + 64]
AB = √89
The length of line segment A'B' is calculated using the distance formula as well:
A'B' = √[(-6 - 0)^2 + (8 - 0)^2]
A'B' = √[(-6)^2 + 8^2]
A'B' = √[36 + 64]
A'B' = √100
A'B' = 10
To find the scale factor, we can divide the length of A'B' by the length of AB:
Scale Factor = A'B' / AB
Scale Factor = 10 / √89
Therefore, the scale factor used in the dilation of line AB is 10 / √89.