Determine the scale factor used in the dilation of line segment AB , centered at the origin. (1 point)
A. 2
B. 4
C. -4
D. 1/4
A (1,-3)
B (2,-4)
A (4,-12)
B (8,-16)
The distance between the points A and B is given by the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
For the segment AB centered at the origin, the points A and B have the coordinates (1, -3) and (2, -4) respectively.
d = √((2 - 1)^2 + (-4 - (-3))^2)
d = √(1^2 + (-1)^2)
d = √(1 + 1)
d = √2
Now, let's determine the distance between the points A' and B' for the dilated line segment AB' centered at the origin. The coordinates for A' and B' are (4, -12) and (8, -16) respectively.
d' = √((8 - 4)^2 + (-16 - (-12))^2)
d' = √(4^2 + (-4)^2)
d' = √(16 + 16)
d' = √32
The scale factor is given by the ratio of d' to d:
scale factor = d' / d
scale factor = (√32) / (√2)
scale factor = (√(16 * 2)) / (√2)
scale factor = (√16 * √2) / (√2)
scale factor = 4 * 1
scale factor = 4
Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 4.
The correct answer is B. 4.
Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin. (1 point)
A. -3
B. 3
C. -1/3
D. 1/3
A (9,9)
B (6,6)
A (3,3)
B (2,2)
The distance between points A and B is given by the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
For the line segment AB centered at the origin, the points A and B have the coordinates (9, 9) and (6, 6) respectively.
d = √((6 - 9)^2 + (6 - 9)^2)
d = √((-3)^2 + (-3)^2)
d = √(9 + 9)
d = √18
Now, let's determine the distance between points A' and B' for the dilated line segment AB with a center point of dilation at the origin. The coordinates for A' and B' are (3, 3) and (2, 2) respectively.
d' = √((2 - 3)^2 + (2 - 3)^2)
d' = √((-1)^2 + (-1)^2)
d' = √(1 + 1)
d' = √2
The scale factor is given by the ratio of d' to d:
scale factor = d' / d
scale factor = (√2) / (√18)
scale factor = (√(2/18))
scale factor = (√(1/9))
scale factor = (√(1/3^2))
scale factor = (√1) / 3
scale factor = 1/3
Therefore, the scale factor used in the dilation of line segment AB, with a center point of dilation at the origin, is 1/3.
The correct answer is D. 1/3.
Describe the sequence of transformations that exhibits the similarity between Figures 1 and 2. (1 point) Responses translation and dilation translation and dilation dilation and reflection dilation and reflection reflection and translation reflection and translation rotation and dilation
The correct sequence of transformations that exhibits the similarity between Figures 1 and 2 is dilation and translation.
Dilation is the transformation that changes the size of the figure while maintaining its shape. Translation is the transformation that moves the figure without changing its shape or size.
In this case, Figure 2 is a scaled and translated version of Figure 1. The dilation changes the size of the figure, making it larger or smaller, and the translation moves the figure to a different position.
So, the correct answer is "dilation and translation".
Dana draws an F on a clear piece of plastic. Which transformation would fail to preserve congruence?(1 point) Responses moving the piece of plastic down and to the left moving the piece of plastic down and to the left looking at the F through a magnifying glass looking at the F through a magnifying glass turning the piece of plastic over turning the piece of plastic over turning the piece of plastic upside down
The transformation that would fail to preserve congruence is "turning the piece of plastic upside down".
When you turn the piece of plastic upside down, the orientation of the F would be reversed. The parts of the F that were originally on top would now be at the bottom, and vice versa. This transformation changes the relative positions of the parts of the F and therefore does not preserve congruence.