Point A is at $(2 ,9 )$ and point B is at $(-8 ,-3 )$ . 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 · 2017-07-08T13:54:24

The new coordinates are $=(9,-2)$ and the distance has changed by $=1.41$

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

The coordinates of $A'$ are

$((0,1),(-1,0))*((2),(9))=((9),(-2))$

Distance $AB$ is

$=sqrt((-8-2)^2+(-3-9)^2)$

$=sqrt(244)$

Distance $A'B$ is

$=sqrt((-8-9)^2+(-3+2)^2)$

$=sqrt290$

The distance has changed by

$=sqrt290-sqrt244$

$=1.41$

Point A is at (2 ,9 )(2 ,9 ) and point B is at (-8 ,-3 )(-8 ,-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?