Dilations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
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)
3 answers
The length of line segment AB can be found using 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 line segment A'B' can be found using the same 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 is 6√2 / 2√2 = 6/2 = 3.