Point A is at #(-2 ,-4 )# and point B is at #(-3 ,3 )#. 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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Mar 20, 2018

Answer:

Increase in distance due to the rotation of point A is

#color(green)(vec(A'B) - vec(AB) = sqrt74 - sqrt50 = 1.53#

Explanation:

http://sites.austincc.edu/tsiprep/math-review/graphing/the-rectangular-coordinate-system-and-point-plotting/

#"Point " A (-2, -4), "Point " B (-3, 3)#

Point A rotated about origin by #(3pi)/2# clockwise.

To find change in distance between Ab due to rotation of point A.

#A (-2, -4) -> A' (4,-2) , " shifted from III to IV quadrant"#

Using distance formula,

#vec(AB) = sqrt((-2+3)^2 + (-4-3)^2) = sqrt50#

#vec(A'B) = sqrt((4+3)^2 + (-2-3)^2) = sqrt74#

Increase in distance due to the rotation of point A is

#color(green)(vec(A'B) - vec(AB) = sqrt74 - sqrt50 = 1.53#

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