Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A(3,7) and B(4,9) .(1 point)
Responses
A′(32,72) and B′(2,92)
upper A prime left parenthesis Start Fraction 3 over 2 End Fraction comma Start Fraction 7 over 2 End Fraction right parenthesis and upper B prime left parenthesis 2 comma Start Fraction 9 over 2 End Fraction right parenthesis
A′(6,14) and B′(−4,3)
upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis
A′(−6,3) and B′(8,18)
upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis
A′(6,14) and B′(8,18)
upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis
The correct answer is:
A′(6,14) and B′(8,18)
upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis
Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13, centered at the origin where the endpoints are A(−6,3) and B(−12,9).(1 point)
Responses
A′(−2,1) and B′(−12,9) upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 12 comma 9 right parenthesis
A′(−6,3) and B′(−4,3)
upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis
A′(−2,1) and B′(−4,3)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis
A′(−18,9) and B′(−36,27)
upper A prime left parenthesis negative 18 comma 9 right parenthesis and upper B prime left parenthesis negative 36 comma 27 right parenthesis
The correct answer is:
A′(−2,1) and B′(−4,3)
upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis
he side lengths of triangle ABC are 10, 14, and 16. The side lengths of triangle A′B′C′ are 35, 49, and 56. Identify the scale factor of a single dilation between the preimage ABC and image A′B′C′ .(1 point)
Responses
3.5
3.5
5.6
5.6
27
Start Fraction 2 over 7 End Fraction
3
To find the scale factor of a dilation between two triangles, we can divide the corresponding side lengths of the image triangle by the corresponding side lengths of the preimage triangle.
In this case, the side lengths of triangle ABC are 10, 14, and 16, and the side lengths of triangle A'B'C' are 35, 49, and 56.
Dividing the corresponding side lengths, we get:
35/10 = 3.5
49/14 = 3.5
56/16 = 3.5
So, the scale factor of the dilation between triangle ABC and triangle A'B'C' is 3.5.
Describe the dilation of triangle ABC , with a scale factor of 5 and a center point of dilation at the origin (0, 0) . (1 point)
Responses
Triangle A′B′C′ is 5 times as large as triangle ABC and is 5 times closer to the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times as large as triangle upper A upper B upper C and is 5 times closer to the center point of dilation.
Triangle A′B′C′ is 5 times as large as triangle ABC and is 5 times as far from the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times as large as triangle upper A upper B upper C and is 5 times as far from the center point of dilation.
Triangle A′B′C′ is 5 times smaller than triangle ABC and is 5 times closer to the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times smaller than triangle upper A upper B upper C and is 5 times closer to the center point of dilation.
Triangle A′B′C′ is 5 times smaller than triangle ABC and is 5 times as far from the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times smaller than triangle upper A upper B upper C and is 5 times as far from the center point of dilation.
The correct answer is:
Triangle A′B′C′ is 5 times larger than triangle ABC and is 5 times closer to the center point of dilation.
Triangle upper A prime upper B prime upper C prime is 5 times as large as triangle upper A upper B upper C and is 5 times closer to the center point of dilation.