Point A is at $(6 ,4 )$ and point B is at $(-2 ,7 )$ . 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 · 2018-03-29T07:52:50

$color(brown)("Decrease in distance due to rotation "$

$color(green)(= vec (AB) - vec(A'B) = 8.54 - 2.24 = 6.3 " units"$

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/U3wqLZDTKqMygVfW5llb_rotation%20rules.jpg)

$A (6,4), B (-2, 7)$

$"A rotated about origin by " (3pi)/2 " clockwise"$

$vec (AB) ' sqrt((6+2)^2 + (4-7)^2) = 8.54 " units"$

$A (6,4) -> A'(-4, 6), " rotated clockwise by " (3pi)/2 " about origin"$

$vec (A'B) = sqrt((-4+2)^2 + (6-7)^2) = 2.24 " units"$

$color(brown)("Decrease in distance due to rotation "$

$color(green)(= vec (AB) - vec(A'B) = 8.54 - 2.24 = 6.3 " units"$

Point A is at (6 ,4 )(6 ,4 ) and point B is at (-2 ,7 )(-2 ,7 ). 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?