Transformations and Similarity Unit Test
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Question
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows ranging from 15 to negative 4 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted in quadrant 1. Point upper A is plotted as left parenthesis 9 comma 9 right parenthesis and point upper B is plotted as left parenthesis 6 comma 6 right parenthesis. The points are plotted on a line segment. Point upper A prime is plotted as left parenthesis 3 comma 3 right parenthesis and upper B prime is plotted as left parenthesis 2 comma 2 right parenthesis. The points are plotted on a line segment.
Determine the scale factor used in the dilation of line segment AB , with a center point of dilation at the origin.
(1 point)
Responses
13
Start Fraction 1 over 3 End Fraction
3
3
−13
negative Start Fraction 1 over 3 End Fraction
−3
negative 3
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The correct answer is 3.
Triangle ABC has vertices point A(−2,−2) , point B(−4,−3) , and point C(−2,−5) . Find the coordinates of A′ , B′ , and C′ after a dilation with a scale factor of 3
and a center point of dilation at the origin.(2 points)
A′= (
)
B′= (
)
C′= (
)
To find the coordinates of the new points after a dilation with a scale factor of 3 and a center point at the origin, you need to multiply the coordinates of the original points by the scale factor.
For point A(-2, -2):
A' = (3*(-2), 3*(-2)) = (-6, -6)
For point B(-4, -3):
B' = (3*(-4), 3*(-3)) = (-12, -9)
For point C(-2, -5):
C' = (3*(-2), 3*(-5)) = (-6, -15)
Therefore:
A' = (-6, -6)
B' = (-12, -9)
C' = (-6, -15)