Question
what are the coordinates of A' if A (5, 6) undergoes a rotation of:
90 degrees clockwise
270 degrees clockwise
90 degrees clockwise
270 degrees clockwise
Answers
Answer
what are the coordinates of A' if A (5, 6) undergoes a rotation of:
180 degrees clockwise
180 degrees counterclockwise
180 degrees clockwise
180 degrees counterclockwise
Answer
what are the coordinates of A' if A (5, 6) undergoes a rotation of:
90 degrees clockwise
180 degrees clockwise
270 degrees clockwise
90 degrees clockwise
180 degrees clockwise
270 degrees clockwise
Answer
if AB = 27 inches, then find the distance of A'B' after a reflection over the x-axis and a translation of (x + 6, y - 2)
A'B' = ___
A'B' = ___
Answer
wrong
Answer
what is the final position of point A (7, 8) after a translation of 2 units left, 1 unit down, and followed by a 180 degrees clockwise rotation around the orgin?
A' = __
A' = __
Answered by
GPT 3.5
To find the coordinates of a point A' after a rotation, you can use the rotation formulas:
For a 90-degree clockwise rotation:
A' = (x, y) -> A' = (y, -x)
For a 270-degree clockwise rotation:
A' = (x, y) -> A' = (-y, x)
Given point A (5, 6), let's find its new coordinates after the rotations:
1. 90 degrees clockwise rotation:
A' = (y, -x) = (6, -5)
Therefore, A' after a 90-degree clockwise rotation is (6, -5).
2. 270 degrees clockwise rotation:
A' = (-y, x) = (-6, 5)
Therefore, A' after a 270-degree clockwise rotation is (-6, 5).
For a 90-degree clockwise rotation:
A' = (x, y) -> A' = (y, -x)
For a 270-degree clockwise rotation:
A' = (x, y) -> A' = (-y, x)
Given point A (5, 6), let's find its new coordinates after the rotations:
1. 90 degrees clockwise rotation:
A' = (y, -x) = (6, -5)
Therefore, A' after a 90-degree clockwise rotation is (6, -5).
2. 270 degrees clockwise rotation:
A' = (-y, x) = (-6, 5)
Therefore, A' after a 270-degree clockwise rotation is (-6, 5).
Answered by
GPT 3.5
To find the coordinates of a point A' after a rotation, you can use the rotation formulas:
For a 180-degree clockwise rotation:
A' = (x, y) -> A' = (-x, -y)
For a 180-degree counterclockwise rotation:
A' = (x, y) -> A' = (-x, -y)
Given point A (5, 6), let's find its new coordinates after the rotations:
1. 180 degrees clockwise rotation:
A' = (-x, -y) = (-5, -6)
Therefore, A' after a 180-degree clockwise rotation is (-5, -6).
2. 180 degrees counterclockwise rotation:
A' = (-x, -y) = (-5, -6)
Therefore, A' after a 180-degree counterclockwise rotation is (-5, -6).
For a 180-degree clockwise rotation:
A' = (x, y) -> A' = (-x, -y)
For a 180-degree counterclockwise rotation:
A' = (x, y) -> A' = (-x, -y)
Given point A (5, 6), let's find its new coordinates after the rotations:
1. 180 degrees clockwise rotation:
A' = (-x, -y) = (-5, -6)
Therefore, A' after a 180-degree clockwise rotation is (-5, -6).
2. 180 degrees counterclockwise rotation:
A' = (-x, -y) = (-5, -6)
Therefore, A' after a 180-degree counterclockwise rotation is (-5, -6).
Answered by
GPT 3.5
To find the coordinates of a point A' after a rotation, you can use the rotation formulas:
For a 90-degree clockwise rotation:
A' = (x, y) -> A' = (y, -x)
For a 180-degree clockwise rotation:
A' = (x, y) -> A' = (-x, -y)
For a 270-degree clockwise rotation:
A' = (x, y) -> A' = (-y, x)
Given point A (5, 6), let's find its new coordinates after the rotations:
1. 90 degrees clockwise rotation:
A' = (y, -x) = (6, -5)
Therefore, A' after a 90-degree clockwise rotation is (6, -5).
2. 180 degrees clockwise rotation:
A' = (-x, -y) = (-5, -6)
Therefore, A' after a 180-degree clockwise rotation is (-5, -6).
3. 270 degrees clockwise rotation:
A' = (-y, x) = (-6, 5)
Therefore, A' after a 270-degree clockwise rotation is (-6, 5).
For a 90-degree clockwise rotation:
A' = (x, y) -> A' = (y, -x)
For a 180-degree clockwise rotation:
A' = (x, y) -> A' = (-x, -y)
For a 270-degree clockwise rotation:
A' = (x, y) -> A' = (-y, x)
Given point A (5, 6), let's find its new coordinates after the rotations:
1. 90 degrees clockwise rotation:
A' = (y, -x) = (6, -5)
Therefore, A' after a 90-degree clockwise rotation is (6, -5).
2. 180 degrees clockwise rotation:
A' = (-x, -y) = (-5, -6)
Therefore, A' after a 180-degree clockwise rotation is (-5, -6).
3. 270 degrees clockwise rotation:
A' = (-y, x) = (-6, 5)
Therefore, A' after a 270-degree clockwise rotation is (-6, 5).
Answered by
GPT 3.5
To find the distance of A'B' after a reflection over the x-axis and a translation of (x + 6, y - 2), we need to perform each transformation step by step.
1. Reflection over the x-axis:
The reflection over the x-axis flips the y-coordinate of each point. So, if A(x, y) is reflected over the x-axis, the new point will be A'(x, -y).
2. Translation of (x + 6, y - 2):
The translation involves shifting each point by the specified amounts. So, after the translation, if A'(x, -y) was A's position, the new point will be A''(x + 6, -y - 2).
Given AB = 27 inches, the distance of A'B' can be found using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, A'B' = A''B'', so we can use A'' and B'' as the coordinates to find the distance.
Given A(x, y), which is the original point A(5, 6), let's find the coordinates of A'B' step by step:
1. Reflection over the x-axis:
A'(x, -y) = (5, -6)
2. Translation of (x + 6, y - 2):
A''(x + 6, -y - 2) = (5 + 6, -(-6) - 2) = (11, 4)
Now, we can find the distance of A''B'', which represents the new A'B', using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(11 - 5)^2 + (4 - 6)^2]
Distance = √[6^2 + (-2)^2]
Distance = √[36 + 4]
Distance = √40
Distance = 2√10
Therefore, the distance of A'B' after a reflection over the x-axis and a translation of (x + 6, y - 2) is 2√10 inches.
1. Reflection over the x-axis:
The reflection over the x-axis flips the y-coordinate of each point. So, if A(x, y) is reflected over the x-axis, the new point will be A'(x, -y).
2. Translation of (x + 6, y - 2):
The translation involves shifting each point by the specified amounts. So, after the translation, if A'(x, -y) was A's position, the new point will be A''(x + 6, -y - 2).
Given AB = 27 inches, the distance of A'B' can be found using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, A'B' = A''B'', so we can use A'' and B'' as the coordinates to find the distance.
Given A(x, y), which is the original point A(5, 6), let's find the coordinates of A'B' step by step:
1. Reflection over the x-axis:
A'(x, -y) = (5, -6)
2. Translation of (x + 6, y - 2):
A''(x + 6, -y - 2) = (5 + 6, -(-6) - 2) = (11, 4)
Now, we can find the distance of A''B'', which represents the new A'B', using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(11 - 5)^2 + (4 - 6)^2]
Distance = √[6^2 + (-2)^2]
Distance = √[36 + 4]
Distance = √40
Distance = 2√10
Therefore, the distance of A'B' after a reflection over the x-axis and a translation of (x + 6, y - 2) is 2√10 inches.
Answered by
GPT 3.5
Apologies for the mistake. Let's go through the transformation steps again:
1. Reflection over the x-axis:
The reflection over the x-axis flips the y-coordinate of each point. So, if A(x, y) is reflected over the x-axis, the new point will be A'(x, -y).
Given point A(5, 6), after reflecting over the x-axis, A' will be (5, -6).
2. Translation of (x + 6, y - 2):
The translation involves shifting each point by the specified amounts. So, after the translation, if A'(x, -y) was A's position, the new point will be A''(x + 6, -y - 2).
Given point A'(5, -6), after the translation, A'' will be (5 + 6, -(-6) - 2) = (11, 4).
Now, let's find the distance between A' and B', which represents the new A'B':
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(11 - 5)^2 + (4 - 6)^2]
Distance = √[6^2 + (-2)^2]
Distance = √[36 + 4]
Distance = √40
Distance = 2√10
Therefore, the distance of A'B' after a reflection over the x-axis and a translation of (x + 6, y - 2) is 2√10 inches.
1. Reflection over the x-axis:
The reflection over the x-axis flips the y-coordinate of each point. So, if A(x, y) is reflected over the x-axis, the new point will be A'(x, -y).
Given point A(5, 6), after reflecting over the x-axis, A' will be (5, -6).
2. Translation of (x + 6, y - 2):
The translation involves shifting each point by the specified amounts. So, after the translation, if A'(x, -y) was A's position, the new point will be A''(x + 6, -y - 2).
Given point A'(5, -6), after the translation, A'' will be (5 + 6, -(-6) - 2) = (11, 4).
Now, let's find the distance between A' and B', which represents the new A'B':
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(11 - 5)^2 + (4 - 6)^2]
Distance = √[6^2 + (-2)^2]
Distance = √[36 + 4]
Distance = √40
Distance = 2√10
Therefore, the distance of A'B' after a reflection over the x-axis and a translation of (x + 6, y - 2) is 2√10 inches.
Answered by
GPT 3.5
To find the final position of point A (7, 8) after a translation of 2 units left and 1 unit down, followed by a 180-degree clockwise rotation, we will perform these transformations one by one.
1. Translation of 2 units left and 1 unit down:
To translate a point, we subtract the specified amounts from the x and y coordinates. So, after the translation, the new point A' will be (7 - 2, 8 - 1), which simplifies to (5, 7).
2. 180-degree clockwise rotation around the origin:
To rotate a point 180 degrees clockwise around the origin, we change the sign of both coordinates. So, after the rotation, the new point A'' will be (-5, -7).
Therefore, the final position of point A (7, 8) after the translation and rotation is A''(-5, -7).
1. Translation of 2 units left and 1 unit down:
To translate a point, we subtract the specified amounts from the x and y coordinates. So, after the translation, the new point A' will be (7 - 2, 8 - 1), which simplifies to (5, 7).
2. 180-degree clockwise rotation around the origin:
To rotate a point 180 degrees clockwise around the origin, we change the sign of both coordinates. So, after the rotation, the new point A'' will be (-5, -7).
Therefore, the final position of point A (7, 8) after the translation and rotation is A''(-5, -7).
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