Dilations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items
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)
The scale factor is
.
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To find the scale factor used in the dilation of line segment AB, we can compare the lengths of the original line segment AB and the dilated line segment A' B'.
The length of line segment AB can be found using the distance formula:
AB = sqrt((4-2)^2 + (1-3)^2) = sqrt((2)^2 + (-2)^2) = sqrt(4 + 4) = sqrt(8)
The length of line segment A' B' can be found using the distance formula as well:
A' B' = sqrt((12-6)^2 + (3-9)^2) = sqrt((6)^2 + (-6)^2) = sqrt(36 + 36) = sqrt(72).
The scale factor is the ratio of the lengths of the dilated line segment to the original line segment:
Scale factor = A' B' / AB = sqrt(72) / sqrt(8) = sqrt(9) = 3.
Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 3.
Dilations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 11 to 10 in 1 unit increments and a y axis capped with arrows and ranging from 12 to negative 12 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted. A coordinate plane with four quadrants shows an x axis capped with arrows and ranging from negative 11 to 10 in 1 unit increments and a y axis capped with arrows and ranging from 12 to negative 12 in 1 unit increments. Point upper A is plotted as left parenthesis negative 3 comma 4 right parenthesis and point upper B is plotted as left parenthesis 2 comma negative 4 right parenthesis. The points are joined by a line that extends beyond the points and is capped with arrows at both ends. Point upper A prime is plotted as left parenthesis negative 6 comma 8 right parenthesis and point upper B prime is plotted as left parenthesis 4 comma negative 8 right parenthesis. The points are joined by a line that extends beyond the points and is capped with arrows at both ends.
Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin.
(1 point)
The scale factor is
.
Skip to navigation
To find the scale factor used in the dilation of line segment AB, we can compare the lengths of the original line segment AB and the dilated line segment A' B'.
The length of line segment AB can be found using the distance formula:
AB = sqrt((2-(-3))^2 + (-4-4)^2) = sqrt((5)^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)
The length of line segment A' B' can be found using the distance formula as well:
A' B' = sqrt((4-(-6))^2 + (-8-8)^2) = sqrt((10)^2 + (-16)^2) = sqrt(100 + 256) = sqrt(356).
The scale factor is the ratio of the lengths of the dilated line segment to the original line segment:
Scale factor = A' B' / AB = sqrt(356) / sqrt(89) = sqrt(4) = 2.
Therefore, the scale factor used in the dilation of line segment AB, with a center point of dilation at the origin, is 2.