Point A is at $(2 ,-4 )$ and point B is at $(1 ,8 )$ . 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?

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Answer 1 · 2018-02-22T06:17:28

Decrease in distance due to rotation of point A about origin is

7.0416

Given : $A (2, -4), B (1,8)$ Point A rotated clockwise about origin by $pi$ .

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$A’(2,-4) -> A’ (-2, 4)$ From IV quadrant to II.

$vec(AB) = sqrt((2-1)^2 + (-4-8)^2) = sqrt145 = 12.0416$

$vec(A’B) = sqrt((-2-1)^2 + (4-8)^2) = 5$

Change is distance

$vec (A’B) - vec(AB) = 5 - 12.0416 = - -7.0416$

Point A is at (2 ,-4 )(2 ,-4 ) and point B is at (1 ,8 )(1 ,8 ). Point A is rotated pi 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?