Point A is at $(8, 7)$ $(8 ,7 )$ and point B is at $(- 3, 9)$ $(-3 ,9 )$ . 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 · 2018-02-07T03:18:58

New coordinates of Point $color(red)(A ((-7),(8))$

Change (reduction) in distance due to rotation between A - B is

$color(green)(11.18 - 4.12 = 7.06)$

A (8,7), B(-3,9). Rotated clockwise about origin by $(3pi)/2$

Distance $vec(AB) = sqrt((8+3)^2 + (7-9)^2) = sqrt125 ~~ color(blue(11.18)$

$A ((8),(7)) to A' ((-7),(8))$ Moved from IV to I quadrant

Distance $vec(A'B) = sqrt((-7+3)^2 + (8-9)^2) = sqrt17 ~~ color(blue(4.12)$

Change (reduction) in distance due to rotation

$color(green)(11.18 - 4.12 = 7.06)$

Point A is at (8 ,7 )(8,7)(8 ,7 ) and point B is at (-3 ,9 )(−3,9)(-3 ,9 ). 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?