To determine the scale factor used in the dilation of line AB, we can compare the lengths of line AB and line A' B'.
The length of line AB can be calculated using the distance formula:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
AB = √[(2 - (-3))^2 + ((-4) - 4)^2]
AB = √[(5)^2 + (-8)^2]
AB = √[25 + 64]
AB = √89
The length of line A' B' can also be calculated using the distance formula:
A' B' = √[(x2 - x1)^2 + (y2 - y1)^2]
A' B' = √[(4 - (-6))^2 + ((-8) - 8)^2]
A' B' = √[(10)^2 + (-16)^2]
A' B' = √[100 + 256]
A' B' = √356
Therefore, the scale factor is AB / A' B':
The scale factor = AB / A' B' = √89 / √356
To simplify the expression, we can rationalize the denominator:
The scale factor = (√89 / √356) * (√356 / √356)
The scale factor = √(89 * 356) / √(356 * 356)
The scale factor = √(31,684) / 356
The scale factor ≈ 5.619 / 356
The scale factor ≈ 0.0158 (rounded to four decimal places)
Therefore, the scale factor used in the dilation of line AB, with a center point of dilation at the origin, is approximately 0.0158.
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
.
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3 answers
nope , try again
Apologies for the previous incorrect response.
To determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin, we can compare the distances between the origin and each point.
The distance between the origin and point A can be calculated using the distance formula:
OA = √[(x1 - 0)^2 + (y1 - 0)^2]
OA = √[(-3)^2 + (4)^2]
OA = √[9 + 16]
OA = √25
OA = 5
The distance between the origin and point A' can also be calculated using the distance formula:
OA' = √[(x1 - 0)^2 + (y1 - 0)^2]
OA' = √[(-6)^2 + (8)^2]
OA' = √[36 + 64]
OA' = √100
OA' = 10
Therefore, the scale factor is OA' / OA:
The scale factor = OA' / OA = 10 / 5
The scale factor = 2
Therefore, the scale factor used in the dilation of line AB, with a center point of dilation at the origin, is 2.
To determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin, we can compare the distances between the origin and each point.
The distance between the origin and point A can be calculated using the distance formula:
OA = √[(x1 - 0)^2 + (y1 - 0)^2]
OA = √[(-3)^2 + (4)^2]
OA = √[9 + 16]
OA = √25
OA = 5
The distance between the origin and point A' can also be calculated using the distance formula:
OA' = √[(x1 - 0)^2 + (y1 - 0)^2]
OA' = √[(-6)^2 + (8)^2]
OA' = √[36 + 64]
OA' = √100
OA' = 10
Therefore, the scale factor is OA' / OA:
The scale factor = OA' / OA = 10 / 5
The scale factor = 2
Therefore, the scale factor used in the dilation of line AB, with a center point of dilation at the origin, is 2.
1 answer