Point A is at (4 ,-2 ) and point B is at (5 ,-4 ). 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?

1 Answer
sankarankalyanam
Jun 30, 2018

color(violet)(0.76 " is the change in the distance between A & B" color(violet)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"

Explanation:

A (4, -2), B (5, -4), " A rotated "(3pi)/2 " clockwise about origin"

#"To find change in distance of AB"

Using distance formula between two points,

bar(AB) = sqrt ((4-5)^2 + (-2 + 4)^2) ~~ 2.24

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/VA3bKvvS3K8G1tSlViNi_rotation%20rules.jpg)

A (4, -2) to A'(2, -4), " as per rotation rule"

bar (A'B) = sqrt((2-5)^2 + (-4+4)^2) = 3

"Change in distance "= 3 - 2.24 = 0.76

color(violet)(0.76 " is the change in the distance between A & B" color(violet)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"

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