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)
To determine the scale factor, we can compare the distances between the original points and the corresponding points after dilation.
The distance between point A and the origin is sqrt((-3-0)^2 + (4-0)^2) = 5.
The distance between point A' and the origin is sqrt((-6-0)^2 + (8-0)^2) = 10.
Therefore, the scale factor is 10/5 = 2.
The scale factor used in the dilation of line AB, with a center point of dilation at the origin, is 2.