Point A is at $(3 ,9 )$ and point B is at $(-2 ,5 )$ . 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?

Question

1372 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-29T10:30:18

The new coordinates of $A=(9,-3)$ and the change in the distance is $=7.2$

The matrix of a rotation clockwise by $1/2pi$ about the origin is

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

Therefore, the trasformation of point $A$ into $A'$ is

$A'=((0,1),(-1,0))((3),(9))=((9),(-3))$

Distance $AB$ is

$=sqrt((-2-3)^2+(5-(9))^2)$

$=sqrt(25+16)$

$=sqrt41$

Distance $A'B$ is

$=sqrt((-2-9)^2+(5-(-3))^2)$

$=sqrt(121+64)$

$=sqrt185$

The distance has changed by

$=sqrt185-sqrt41$

$=7.2$

Point A is at (3 ,9 )(3 ,9 ) and point B is at (-2 ,5 )(-2 ,5 ). 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?