To determine the scale factor used in the dilation of line segment AB, we need to find the ratio of the lengths of line segment A'B' to AB.
The length of AB can be found 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 be found using the distance formula as well:
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 = √(16 * 2) = 4√2
The scale factor is the ratio of A'B' to AB:
Scale factor = A'B' / AB
Scale factor = (4√2) / √2
Scale factor = 4√2 / √2
The square roots cancel out:
Scale factor = 4
Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 4.
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)
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1 answer