# Point A is at #(-2 ,-8 )# and point B is at #(-5 ,3 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

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The distance between points A and B remains the same after the rotation since it is unaffected byThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotationThe new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformationsThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations aboutThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

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For a pointThe new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin.The new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore,The new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (xThe new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, theThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x,The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distanceThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, yThe new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance betweenThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y)The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance between pointsThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y) \The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance between points AThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y) )The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance between points A andThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y) ) rotatedThe new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance between points A and B remainsThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y) ) rotated byThe new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance between points A and B remains constantThe new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y) ) rotated by an angleThe new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance between points A and B remains constant.The new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y) ) rotated by an angle ( \The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (8, -2). The distance between points A and B remains the same after the rotation since it is unaffected by rotational transformations about the origin. Therefore, the distance between points A and B remains constant.The new coordinates of point A after rotating it ( \frac{3\pi}{2} ) clockwise about the origin are (8, -2). To find the new coordinates, we use the rotation formulas:

For a point ( (x, y) ) rotated by an angle ( \theta ) clockwise about the origin, the new coordinates ( (x', y') ) are given by: [ x' = x \cos(\theta) - y \sin(\theta) ] [ y' = x \sin(\theta) + y \cos(\theta) ]

Using these formulas with ( (x, y) = (-2, -8) ) and ( \theta = \frac{3\pi}{2} ), we get: [ x' = -2 \cos\left(\frac{3\pi}{2}\right) - (-8) \sin\left(\frac{3\pi}{2}\right) = -2 \cdot 0 - (-8) \cdot (-1) = 8 ] [ y' = -2 \sin\left(\frac{3\pi}{2}\right) + (-8) \cos\left(\frac{3\pi}{2}\right) = -2 \cdot (-1) + (-8) \cdot 0 = -2 ]

So, the new coordinates of point A are (8, -2).

To find the change in distance between points A and B, we calculate the distances between the original and new coordinates of point A, and between points B and the original coordinates of A:

Original distance between A and B: [ d_{AB} = \sqrt{(-5 - (-2))^2 + (3 - (-8))^2} = \sqrt{(-3)^2 + (11)^2} = \sqrt{9 + 121} = \sqrt{130} ]

New distance between A and B: [ d'_{AB} = \sqrt{(8 - (-5))^2 + (-2 - 3)^2} = \sqrt{(13)^2 + (-5)^2} = \sqrt{169 + 25} = \sqrt{194} ]

The change in distance between A and B is:
[ \Delta d_{AB} = d'*{AB} - d*{AB} = \sqrt{194} - \sqrt{130} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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