Point A is at $(5, 1)$ $(5 ,1 )$ and point B is at $(2, - 4)$ $(2 ,-4 )$ . 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 · 2016-11-24T12:52:08

$The new coordinates of A is (-1,5)$ $"The new coordinates of A is (-1,5)"$

$distance : \sqrt{90}$ $"distance :"sqrt(90)$

$draw A(5,1) and B(2,-4)$ $"draw A(5,1) and B(2,-4)"$

enter image source here

$(2 π) - \frac{3 π}{2} = \frac{π}{2}$ $(2pi)-(3pi)/2=pi/2$

$clockwise \frac{3 π}{2} equals counterclockwise \frac{π}{2}$ $"clockwise "(3pi)/2 " equals counterclockwise "pi/2$

$"so " A(x,y) " "A'(-y,x)$

$"The new Position of A is "A'(-1,5)$

enter image source here

$"distance between B and A' can be calculated using the triangle A'DB"$

$A'B=sqrt(3^2+9^2)$

$A'B=sqrt(9+81)$

$A'B=sqrt(90)$

Point A is at (5 ,1 )(5,1)(5 ,1 ) and point B is at (2 ,-4 )(2,−4)(2 ,-4 ). 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?