To determine the scale factor used in the dilation of line segment AB, we can compare the lengths of AB and A' B'.
The length of AB is given by the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(4 - 2)^2 + (1 - 3)^2]
= √[(2)^2 + (-2)^2]
= √[4 + 4]
= √8 = 2√2
The length of A' B' is given by the distance formula:
A' B' = √[(x2' - x1')^2 + (y2' - y1')^2]
= √[(12 - 6)^2 + (3 - 9)^2]
= √[(6)^2 + (-6)^2]
= √[36 + 36]
= √72 = 6√2
Therefore, the scale factor used in the dilation of line segment AB is 6√2 / 2√2 = 3.
Use the image to answer the question.
A coordinate plane with four quadrants shows x-axis ranging from negative 5 to 12 in increments of 1 and the y-axis from 17 to negative 4 in increments of 1. Points upper A, upper B, upper A prime, and upper B prime are plotted on quadrant 1. The plotted points are as follows: Upper A is left parenthesis 2 comma 3 right parenthesis and upper B is left parenthesis 4 comma 1 right parenthesis. The points are joined by a line. Upper A prime is plotted as left parenthesis 6 comma 9 right parenthesis and upper B prime as left parenthesis 12 comma 3 right parenthesis. The points are joined by a line.
Determine the scale factor used in the dilation of line segment AB , centered at the origin.
(1 point)
The scale factor is ___
3 answers
The answer is 3
Apologies for the error. Yes, the correct scale factor used in the dilation of line segment AB is indeed 3.