Determine the scale factor used in the dilation of line segment AB, centered at the origin. A (4,-12)
B (8,-16)
(1 point)
A. 2
B. 1/4
C. 4
D. -4
To find the scale factor of a dilation, we need to find the ratio of the lengths of the corresponding sides.
The length of AB can be found using the distance formula:
AB = √((x2 - x1)^(2) + (y2 - y1)^(2))
AB = √((8 - 4)^(2) + (-16 - (-12))^(2))
AB = √(4^(2) + (-4)^(2))
AB = √(16 + 16)
AB = √32
AB ≈ 5.66
To find the length of A'B', we need to find the corresponding coordinates after the dilation. Since the line segment is centered at the origin, the coordinates of A' would be (2*4, 2*(-12)) = (8, -24) and the coordinates of B' would be (2*8, 2*(-16)) = (16, -32).
The length of A'B' can be found using the distance formula:
A'B' = √((x2 - x1)^(2) + (y2 - y1)^(2))
A'B' = √((16 - 8)^(2) + (-32 - (-24))^(2))
A'B' = √(8^(2) + (-8)^(2))
A'B' = √(64 + 64)
A'B' = √128
A'B' ≈ 11.31
Therefore, the scale factor is A'B' / AB = 11.31 / 5.66 = 2.
The scale factor used in the dilation of line segment AB, centered at the origin, is 2.
Answer: A. 2
Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin.
A -1/3
B 1/3
C 3
D -3
To find the scale factor of a dilation, we need to find the ratio of the lengths of the corresponding sides.
The length of AB can be found using the distance formula:
AB = √((x2 - x1)^(2) + (y2 - y1)^(2))
AB = √((Bx - Ax)^(2) + (By - Ay)^(2))
AB = √((0 - 1)^(2) + (3 - (-2))^(2))
AB = √((-1)^(2) + 5^(2))
AB = √(1 + 25)
AB = √26
To find the length of A'B', we need to find the corresponding coordinates after the dilation. Since the line segment is centered at the origin, the coordinates of A' would be (k * 1, k * (-2)) = (k, -2k) and the coordinates of B' would be (k * 0, k * 3) = (0, 3k).
The length of A'B' can be found using the distance formula:
A'B' = √((x2 - x1)^(2) + (y2 - y1)^(2))
A'B' = √((0 - k)^(2) + (3k - (-2k))^(2))
A'B' = √((-k)^(2) + (5k)^(2))
A'B' = √(k^(2) + 25k^(2))
A'B' = √(26k^(2))
Therefore, the scale factor is A'B' / AB = √(26k^(2)) / √26 = √(k^(2) * 26) / √26 = √k^(2) = k.
The scale factor used in the dilation of line AB, centered at the origin, is k.
From the given options, it is clear that the correct answer is:
Answer: C. 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)
To find the coordinates after a dilation with a scale factor of 3 and a center point of dilation at the origin, we need to multiply the x and y coordinates of each vertex by the scale factor.
Let's find the coordinates of A' first:
x coordinate of A' = (-2) * 3 = -6
y coordinate of A' = (-2) * 3 = -6
Therefore, the coordinates of A' are (-6, -6).
Next, let's find the coordinates of B':
x coordinate of B' = (-4) * 3 = -12
y coordinate of B' = (-3) * 3 = -9
Therefore, the coordinates of B' are (-12, -9).
Finally, let's find the coordinates of C':
x coordinate of C' = (-2) * 3 = -6
y coordinate of C' = (-5) * 3 = -15
Therefore, the coordinates of C' are (-6, -15).
So, the coordinates of A' are (-6, -6), the coordinates of B' are (-12, -9), and the coordinates of C' are (-6, -15).
Answer: A'(-6, -6), B'(-12, -9), C'(-6, -15).
Dana draws an F on a clear piece of plastic. Which transformation would fail to preserve congruence?
looking at the F through a magnifying glass
turning the piece of plastic upside down
• turning the piece of plastic over
moving the piece of plastic down and to the left
The transformation that would fail to preserve congruence is "looking at the F through a magnifying glass".
When looking at an object through a magnifying glass, the size of the object appears larger. This is a type of dilation, which changes the size but not the shape of the object. Therefore, the magnified image of the F would be similar to the original F, but not congruent to it.
The other transformations mentioned, such as turning the piece of plastic upside down, turning it over, and moving it down and to the left, do not change the shape of the F. In these transformations, the size and orientation of the F remain the same, so the congruence is preserved.
If you would like to dilate a square with a side length of 8 units to create a square with a side length of 20 units, what scale factor should you use? Write your answer in decimal form. (1 point)
To find the scale factor, we can divide the length of the new square by the length of the original square:
Scale factor = Length of new square / Length of original square
In this case, the length of the new square is 20 units, and the length of the original square is 8 units. Therefore:
Scale factor = 20 / 8
Scale factor = 2.5
Therefore, the scale factor to dilate the square with a side length of 8 units to create a square with a side length of 20 units is 2.5 (in decimal form).
hich equation shows the relation between the vertices of a dilated figure and the vertices of the iginal figure when the original figure is dilated using a scale factor of 5? (1 point)
О У2 = 522, У = 521
• (22, y2) = (21 + 5, 41 + 5)
• (X2, 32) = (521, 541)
О У2 = 22 + 5,31 = 21 + 5