Point A is at $(8 ,4 )$ and point B is at $(-3 ,1 )$ . 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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Answer 1 · 2018-02-16T14:57:22

New coordinates of A $(-4,8)$ . There is no change in distance between AB & A’B.

Given : A (8,4), B (-3,1), A rotated by $(3pi)/2$ clockwise about the origin.

To find A’, change in distance between A & B

Using distance formula,

$vec(AB) = sqrt((8+3)^2 + (4-1)^2) = sqrt130$

New coordinates of A $A’ ((4),(-8))$

$vec(A’B) = sqrt((4+3)^2 + (-8-1)^2) = sqrt(130$

There is no change in the distance between AB due to the rotation.

Point A is at (8 ,4 )(8 ,4 ) and point B is at (-3 ,1 )(-3 ,1 ). Point A is rotated (3pi)/2 (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?