Point A is at $(5 ,2 )$ and point B is at $(-6 ,-4 )$ . Point A is rotated $(3pi)/2$ 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 · 2018-02-10T11:54:35

Distance between A and B changed by $4.47$ unit .

$A(5,2) and B (-6,-4)$ . Clockwise rotation of point A is

$theta=(3pi)/2 :.$ Counterclockwise rotation of point A is

$theta=(2pi)-(3pi)/2=pi/2$ . New coordinates of $A(x',y')$ can be

found by the fomula. $x'= xcos theta +ysin theta$ and

$y'= y cos theta - x sin theta:.x'= 5*cos 90+ 2*sin90$

$:. x'= 5 *0 +2*1=2 ; y'= 2 * cos 90 - 5 * sin 90$ or

$y'= 2 * 0- 5 * 1= -5$ Therefore,new coordinates of A are

$(x',y') = (2,-5)$ 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 $A(5,2) and B (-6,-4)$ is

$D_o= sqrt((5+6)^2+(2+4)^2)=sqrt 157~~ 12.53$ unit.

New distance between points $A(2,-5) and B (-6,-4)$ is

$D_n= sqrt((2+6)^2+(-5+4)^2)=sqrt 65~~ 8.06$ unit.

Distance between A and B changed by $12.53-8.06~~4.47$ unit .

[Ans]

Point A is at (5 ,2 )(5 ,2 ) and point B is at (-6 ,-4 )(-6 ,-4 ). Point A is rotated (3pi)/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?