Point A is at $(3 ,7 )$ and point B is at $(3 ,-4 )$ . 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 · 2018-02-20T12:31:54

New coordinates of point A is $(-7,3)$ and Distance between A and B changed by $1.1$ unit.

$A(3,7) and B (3,-4)$ . Clockwise rotation of point A is

$alpha=pi/2 :.$ Counterclockwise rotation of point A is

$theta=2pi-alpha=2pi-pi/2=(3pi)/2$ . New coordinates of

$A(x',y')$ can be found by the fomula ,

$x'= xcos theta +ysin theta and y'= y cos theta - x sin theta$

$:.x'= 3*cos((3pi)/2)+7*sin((3pi)/2) = 0+(-7)=-7$

$x'= -7; y'= 7* cos((3pi)/2)- 3 * sin((3pi)/2)$

$= 7 * 0-3 *(-1)=3:. y'=3 :. (x',y') = (-7,3)$

Distance between two points $(x_1,y_1) and (x_2,y_2)$ is

$D= sqrt((x_1-x_2)^2+(y_1-y_2)^2)$ . Orginal distance between

points $A(3,7) and B (3,-4)$ is

$D_o= sqrt((3-3)^2+(7+4)^2)=sqrt 121= 11.0$ unit.

New distance between points $A(-7,3) and B (3,-4)$ is

$D_n= sqrt((-7-3)^2+(3+4)^2)=sqrt 149~~ 12.2$ unit

Distance between A and B changed by $12.2-11.1=1.1$ unit .

[Ans]

Point A is at (3 ,7 )(3 ,7 ) and point B is at (3 ,-4 )(3 ,-4 ). 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?