Point A is at $(6, 7)$ $(6 ,7 )$ and point B is at $(- 3, 4)$ $(-3 ,4 )$ . 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 · 2018-02-22T07:20:10

There is a reduction in distance due to rotation of point A by $\frac{3 π}{2}$ $(3pi)/2$ clockwise

$d = 9.4868 - 4.4721 = 5.0147$ $color(blue)(d = 9.4868 - 4.4721 = 5.0147$

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$A (6, 7), B (- 3, 4)$ $A (6,7), B (-3,4)$ . Point A Rotated clockwise by $\frac{3 π}{2}$ $(3pi)/2$ about origin .

$A((6),(7)) -> A’ ((-7),(6))$

$vec(AB) = sqrt((6+3)^2 + (7-4)^2) = 9.4868$

vec(A’B) = sqrt((-7+3)^2 + (6-4)^2) = 4.4721#

There is a reduction in distance due to rotation of point A by $(3pi)/2$ clockwise

$d = 9.4868 - 4.4721 = 5.0147$

Point A is at (6 ,7 )(6,7)(6 ,7 ) and point B is at (-3 ,4 )(−3,4)(-3 ,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?