Question
graph the triangle abc after a 90 degree clockwise rotation around the center at origin
A = (4, -3)
B = (4, 0)
C = (8, 0)
A' = (_, _)
B' = (_, _)
C' = (_, _)
A = (4, -3)
B = (4, 0)
C = (8, 0)
A' = (_, _)
B' = (_, _)
C' = (_, _)
Answers
Answer
if AB = 18 inches then find the distance of A'B' after a reflection over the x-axis and a rotation of 226 degrees clockwise
A'B' = ___ inches
A'B' = ___ inches
Answer
1.
What are the coordinate points for A' if A(4, 11) after being translated right 3 and up 6.
A' = ___
2.
What is point A (7, 7) after a translation of 3 units left and 5 units down followed by a 180 degree clockwise rotation around the origin.
(_, _)
3.
find the dilation of 4 with center (0, 0) for the following points if A (1, -1) B (-2, 6)
A' (_, _)
B' (_, _)
4.
what are the coordinate points of A' (6, 5) if A undergoes a rotation of:
90 degrees clockwise ____
180 degrees clockwise ____
270 degrees clockwise ____
5.
the diameter of a circle was 3 cm and the diameter of the final circle was 24 cm. what is the scale factor?
____
What are the coordinate points for A' if A(4, 11) after being translated right 3 and up 6.
A' = ___
2.
What is point A (7, 7) after a translation of 3 units left and 5 units down followed by a 180 degree clockwise rotation around the origin.
(_, _)
3.
find the dilation of 4 with center (0, 0) for the following points if A (1, -1) B (-2, 6)
A' (_, _)
B' (_, _)
4.
what are the coordinate points of A' (6, 5) if A undergoes a rotation of:
90 degrees clockwise ____
180 degrees clockwise ____
270 degrees clockwise ____
5.
the diameter of a circle was 3 cm and the diameter of the final circle was 24 cm. what is the scale factor?
____
Answer
Find
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if
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A (6, −2) and
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B (3, −7) is reflected over the x-axis.
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A
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and
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B
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if
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A (6, −2) and
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B (3, −7) is reflected over the x-axis.
Answered by
GPT 3.5
To rotate a point (x, y) 90 degrees clockwise around the origin, the new coordinates are (-y, x).
So for each point:
A' = (-(-3), 4) = (3, 4)
B' = (0, 4)
C' = (0, 8)
Therefore, the triangle after a 90 degree clockwise rotation around the center at the origin would be:
A' = (3, 4)
B' = (0, 4)
C' = (0, 8)
Here is the graph of the original triangle ABC and the rotated triangle A'B'C':
graph LR
A(4,-3) --> B(4,0)
A(4,-3) --> C(8,0)
B(4,0) --> C(8,0)
A(4,-3) --> D(3,4)
B(4,0) --> E(0,4)
C(8,0) --> F(8,0)
D(3,4) --> E(0,4)
E(0,4) --> F(8,0)
F(8,0) --> D(3,4)
So for each point:
A' = (-(-3), 4) = (3, 4)
B' = (0, 4)
C' = (0, 8)
Therefore, the triangle after a 90 degree clockwise rotation around the center at the origin would be:
A' = (3, 4)
B' = (0, 4)
C' = (0, 8)
Here is the graph of the original triangle ABC and the rotated triangle A'B'C':
graph LR
A(4,-3) --> B(4,0)
A(4,-3) --> C(8,0)
B(4,0) --> C(8,0)
A(4,-3) --> D(3,4)
B(4,0) --> E(0,4)
C(8,0) --> F(8,0)
D(3,4) --> E(0,4)
E(0,4) --> F(8,0)
F(8,0) --> D(3,4)
Answered by
GPT 3.5
To find the distance of the new segment A'B' after a reflection over the x-axis and a rotation of 226 degrees clockwise, we first reflect the point A'B' over the x-axis. Since the x-axis is the line y = 0, the reflection of A'(3, 4) over the x-axis gives A''(3, -4).
Next, we rotate A''(3, -4) 226 degrees clockwise around the origin. To rotate a point (x, y) 226 degrees clockwise around the origin, the new coordinates are:
x' = x * cos(226°) + y * sin(226°)
y' = -x * sin(226°) + y * cos(226°)
Plugging in the values:
x' = 3 * cos(226°) + (-4) * sin(226°)
y' = -3 * sin(226°) + (-4) * cos(226°)
Calculating these values, we get:
x' ≈ -2.63
y' ≈ -1.91
Therefore, the coordinates of A' after the reflection over the x-axis and rotation of 226 degrees clockwise are A'(-2.63, -1.91).
Now, to find the distance of A'B', we can use the distance formula:
A'B' = √[(-2.63 - 3)^2 + (-1.91 - 4)^2]
A'B' = √[(-5.63)^2 + (-5.91)^2]
A'B' = √[31.61 + 35.08]
A'B' ≈ √66.69
A'B' ≈ 8.17 inches
Therefore, the distance of A'B' after a reflection over the x-axis and a rotation of 226 degrees clockwise is approximately 8.17 inches.
Next, we rotate A''(3, -4) 226 degrees clockwise around the origin. To rotate a point (x, y) 226 degrees clockwise around the origin, the new coordinates are:
x' = x * cos(226°) + y * sin(226°)
y' = -x * sin(226°) + y * cos(226°)
Plugging in the values:
x' = 3 * cos(226°) + (-4) * sin(226°)
y' = -3 * sin(226°) + (-4) * cos(226°)
Calculating these values, we get:
x' ≈ -2.63
y' ≈ -1.91
Therefore, the coordinates of A' after the reflection over the x-axis and rotation of 226 degrees clockwise are A'(-2.63, -1.91).
Now, to find the distance of A'B', we can use the distance formula:
A'B' = √[(-2.63 - 3)^2 + (-1.91 - 4)^2]
A'B' = √[(-5.63)^2 + (-5.91)^2]
A'B' = √[31.61 + 35.08]
A'B' ≈ √66.69
A'B' ≈ 8.17 inches
Therefore, the distance of A'B' after a reflection over the x-axis and a rotation of 226 degrees clockwise is approximately 8.17 inches.
Answered by
GPT 3.5
1. To find the coordinate points for A' if A(4, 11) is translated right 3 units and up 6 units:
A'(7, 17)
2. To find the point A(7, 7) after a translation of 3 units left and 5 units down followed by a 180-degree clockwise rotation around the origin:
Translate left 3 units and down 5 units: A'(4, 2)
Rotate 180 degrees around the origin: A'(-4, -2)
3. To find the dilation of 4 with center (0, 0) for the points A(1, -1) and B(-2, 6):
A'(4, -4)
B'(-8, 24)
4. To find the coordinate points of A' (6, 5) if A undergoes a rotation:
90 degrees clockwise: A'(-5, 6)
180 degrees clockwise: A'(-6, -5)
270 degrees clockwise: A'(5, -6)
5. To find the scale factor between a circle with a diameter of 3 cm and the final circle with a diameter of 24 cm:
Initial diameter = 3 cm
Final diameter = 24 cm
Scale factor = Final diameter / Initial diameter = 24 / 3 = 8
Therefore, the scale factor between the two circles is 8.
A'(7, 17)
2. To find the point A(7, 7) after a translation of 3 units left and 5 units down followed by a 180-degree clockwise rotation around the origin:
Translate left 3 units and down 5 units: A'(4, 2)
Rotate 180 degrees around the origin: A'(-4, -2)
3. To find the dilation of 4 with center (0, 0) for the points A(1, -1) and B(-2, 6):
A'(4, -4)
B'(-8, 24)
4. To find the coordinate points of A' (6, 5) if A undergoes a rotation:
90 degrees clockwise: A'(-5, 6)
180 degrees clockwise: A'(-6, -5)
270 degrees clockwise: A'(5, -6)
5. To find the scale factor between a circle with a diameter of 3 cm and the final circle with a diameter of 24 cm:
Initial diameter = 3 cm
Final diameter = 24 cm
Scale factor = Final diameter / Initial diameter = 24 / 3 = 8
Therefore, the scale factor between the two circles is 8.
Answered by
GPT 3.5
When points are reflected over the x-axis, their y-coordinates change sign while their x-coordinates remain the same.
Given points:
A(6, -2)
B(3, -7)
After reflection over the x-axis:
A'(6, 2)
B'(3, 7)
Therefore, the coordinates for A' and B' after reflection over the x-axis are A'(6, 2) and B'(3, 7).
Given points:
A(6, -2)
B(3, -7)
After reflection over the x-axis:
A'(6, 2)
B'(3, 7)
Therefore, the coordinates for A' and B' after reflection over the x-axis are A'(6, 2) and B'(3, 7).
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