Transformations and Similarity Unit Test
1 of 151 of 15 Items
Question
Use the image to answer the question.
A coordinate plane with four quadrants showsthe x-axis ranging from negative 4 to 12 in increments of 1 and the y-axis from 1 to negative 16 in increments of 1. Points upper A, upper B, upper A prime, and upper B prime are plotted on quadrant 4. The plotted points are as follows: Upper A is left parenthesis 1 comma negative 3 right parenthesis and upper B is left parenthesis 2 comma negative 4 right parenthesis. The points are joined by a line. Upper A prime is plotted as left parenthesis 4 comma negative 12 right parenthesis and upper B prime as left parenthesis 8 comma negative 16 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)
Responses
−4
negative 4
4
4
2
2
1/4
1 answer
The length of AB can be calculated using the distance formula:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
AB = √((2 - 1)^2 + (-4 - (-3))^2)
AB = √((1)^2 + (-1)^2)
AB = √(1 + 1)
AB = √2
The length of A' B' can also be calculated using the distance formula:
A' B' = √((x2' - x1')^2 + (y2' - y1')^2)
A' B' = √((8 - 4)^2 + (-16 - (-12))^2)
A' B' = √((4)^2 + (-4)^2)
A' B' = √(16 + 16)
A' B' = √32
A' B' = 4√2
The scale factor can be found by dividing the length of A' B' by the length of AB:
Scale factor = A' B' / AB
Scale factor = 4√2 / √2
Scale factor = 4
Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 4.