1. Line segment has endpoints of A(1,4) and B(-2,1), It is dilated and A’(3,12) and B(-6,3). What is the scale factor?
To find the scale factor, we need to compare the lengths of the original line segment AB and the dilated line segment A'B'.
The length of AB can be found using the distance formula:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
= √((-2 - 1)^2 + (1 - 4)^2)
= √(9 + 9)
= √18
Similarly, the length of A'B' can be found using the distance formula:
A'B' = √((x2 - x1)^2 + (y2 - y1)^2)
= √((-6 - 3)^2 + (3 - 12)^2)
= √(81 + 81)
= √162
So, the scale factor is the ratio of the lengths of the dilated line segment to the original line segment:
Scale factor = A'B' / AB
= √162 / √18
= (√(9 * 18)) / √(3 * 3 * 2)
= (√(9) * √(18)) / (3 * √(2))
= 3√2 / 3√2
= 1
Therefore, the scale factor is 1.