Transformations and Similarity Unit Test
2 of 152 of 15 Items
Question
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows ranging from 15 to negative 4 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted in quadrant 1. Point upper A is plotted as left parenthesis 9 comma 9 right parenthesis and point upper B is plotted as left parenthesis 6 comma 6 right parenthesis. The points are plotted on a line segment. Point upper A prime is plotted as left parenthesis 3 comma 3 right parenthesis and upper B prime is plotted as left parenthesis 2 comma 2 right parenthesis. The points are plotted on a line segment.
Determine the scale factor used in the dilation of line segment AB , with a center point of dilation at the origin.
(1 point)
Responses
−13
negative Start Fraction 1 over 3 End Fraction
13
Start Fraction 1 over 3 End Fraction
−3
negative 3
3
To find the scale factor used in the dilation of line segment AB with a center point of dilation at the origin, we can compare the lengths of the two line segments after dilation.
The length of AB is: sqrt((9-6)^2 + (9-6)^2) = sqrt(9+9) = sqrt(18)
The length of A'B' is: sqrt((3-2)^2 + (3-2)^2) = sqrt(1+1) = sqrt(2)
The scale factor is the ratio of the lengths: sqrt(2)/sqrt(18) = sqrt(2/18) = sqrt(1/9) = 1/3
So, the scale factor used in the dilation of line segment AB is 1/3.
Therefore, the correct answer is Start Fraction 1 over 3 End Fraction.