Point A is at $(-8 ,-2 )$ and point B is at $(2 ,-3 )$ . Point A is rotated $pi/2$ 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 · 2017-07-14T17:09:21

The new coordinates are $=(-2,8)$ and the distance has changed by $=1.65$

The rotation of $pi/2$ clockwise about the origin transforms the point $A$ into $A'$

The coordinates of $A'$ are

$((0,1),(-1,0))*((-8),(-2))=((-2),(8))$

Distance $AB$ is

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

$=sqrt(100+1)$

$=sqrt(101)$

Distance $A'B$ is

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

$=sqrt(16+121)$

$=sqrt(137)$

The distance has changed by

$=sqrt137-sqrt101$

$=1.65$

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