Point A is at $(- 5, 1)$ $(-5 ,1 )$ and point B is at $(2, - 3)$ $(2 ,-3 )$ . Point A is rotated $\frac{3 π}{2}$ $(3pi)/2$ 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?

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Answer 1 · 2017-06-02T11:40:11

The distance has changed by $= 4.46$ $=4.46$

The matrix of a rotation clockwise by $\frac{3}{2} π$ $3/2pi$ 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 $A$ into $A'$ is

$A'=((0,-1),(1,0))((-5),(1))=((-1),(-5))$

Distance $AB$ is

$=sqrt((2-(-5))^2+(-3-(-1))^2)$

$=sqrt(49+16)$

$=sqrt65$

Distance $A'B$ is

$=sqrt((2-(-1))^2+(-3-(-5))^2)$

$=sqrt(9+4)$

$=sqrt13$

The distance has changed by

$=sqrt65-sqrt13$

$=4.46$

Point A is at (-5 ,1 )(−5,1)(-5 ,1 ) and point B is at (2 ,-3 )(2,−3)(2 ,-3 ). Point A is rotated (3pi)/2 3π2(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?