Point A is at $(2 ,9 )$ and point B is at $(1 ,-3 )$ . Point A is rotated $pi$ 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 · 2018-05-04T03:40:39

$color(maroon)("New coordinates of point A " (-2, -9)$

$color(purple)("Distance between A & B reduced by " color(red)(5.33 units " after point A was rotated by "pi^c$

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$A (2,9), B ((1,-3)$

$bar (AB) = sqrt((x_b-x_a)^2 + (y_b - y_a)^2)$

$bar(AB) = sqrt((1-2)^2 + (-3-9)^2) = 12.04$

Point A rotated by $pi^c$ to point A' with new coordinates,

$A' (x,y) = (-2,-9)$

$bar(A'B) = sqrt(1+2)^2 + (-3+9)^2) = 6.71$

Change in distance between $bar(AB), bar(A'B)$ is

$bar(AB) - bar(A'B) = 12.04 - 6.71 = 5.33$

Point A is at (2 ,9 )(2 ,9 ) and point B is at (1 ,-3 )(1 ,-3 ). Point A is rotated pi pi 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?