Point A is at $(1 ,-8 )$ and point B is at $(-3 ,-2 )$ . 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 · 2017-05-07T17:22:25

The new coordinates are $=(8,1)$ and the change in the distance is $=4.2$

The matrix of a rotation clockwise by $3/2pi$ about the origin is

$=((cos(-3/2pi),-sin(-3/2pi)),(sin(-3/2pi),cos(-3/2pi)))=((0,1),(-1,0))$

Therefore, the trasformation of point $A$ is

$A'=((0,-1),(1,0))((1),(-8))=((8),(1))$

Distance $AB$ is

$=sqrt((-3-1)^2+(-2+8)^2)$

$=sqrt(16+36)$

$=sqrt52$

Distance $A'B$ is

$=sqrt((-3-8)^2+(-2-1)^2)$

$=sqrt(121+9)$

$=sqrt130$

The distance has changed by

$=sqrt130-sqrt52$

$=4.2$

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