Point A is at $(- 5, 4)$ $(-5 ,4 )$ and point B is at $(- 8, 7)$ $(-8 ,7 )$ . 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 · 2018-04-06T08:08:57

$Increase in distance due to the rotation = 8.4065$ $color(indigo)("Increase in distance due to the rotation " = 8.4065$

$A (- 5, 4), B (- 8, 7), rotated \frac{3 π}{2} clockwise about the origin$ $A (-5,4), B(-8,7), " rotated " (3pi)/2 " clockwise about the origin"$

$¯ ¯¯¯¯ ¯ A B = \sqrt{{(- 5 + 8)}^{2} + {(4 - 7)}^{2}} = 4.2426$ $bar(AB) = sqrt((-5+8)^2 + (4-7)^2) = 4.2426$

![https://teacher.desmos.com/activitybuilder/custom/566b16af914c731d06ef1953]( useruploads.socratic.org )

$A (-5, 4) to A'( -4,-5)$

$bar(A'B) = sqrt((-4 + 8)^2 + (-5 - 7)^2) = 12.6491$

$color(indigo)("Increase in distance " = 12.6491 - 4.2426 = 8.4065$

Point A is at (-5 ,4 )(−5,4)(-5 ,4 ) and point B is at (-8 ,7 )(−8,7)(-8 ,7 ). 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?