# Point A is at #(-7 ,-1 )# and point B is at #(2 ,-4 )#. Point A is rotated #pi # 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?

#"To find change in distance of AB"

Using distance formula between two points,

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The new coordinates of point A after rotating π radians clockwise about the origin are (1, 7). To calculate the distance between the new point A and point B, we use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance between the original points A and B:

Distance_AB = √((-7 - 2)^2 + (-1 - (-4))^2) = √((-9)^2 + (3)^2) = √(81 + 9) = √90

Distance_AB ≈ 9.49 units

Distance between the new point A and point B:

Distance_A'B' = √((1 - 2)^2 + (7 - (-4))^2) = √((-1)^2 + (11)^2) = √(1 + 121) = √122

Distance_A'B' ≈ 11.05 units

The change in distance between points A and B is:

ΔDistance = Distance_A'B' - Distance_AB ≈ 11.05 - 9.49 ≈ 1.56 units

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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.

- Please answer my question. It is optional maths?
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