Point A is at (-3 ,-4 ) and point B is at (1 ,8 ). 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?

1 Answer
sankarankalyanam
Jun 30, 2018

color(orange)(8.18 " is the reduction in the distance between A & B" color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"

Explanation:

A (-3, -4), B (1, 8), " A rotated "pi " clockwise about origin"

#"To find change in distance of AB"

Using distance formula between two points,

bar(AB) = sqrt ((-3 -1)^2 + (-4 - 8)^2) ~~ 12.65

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

A (-3, -4) to A'(3, 4), " as per rotation rule"

bar (A'B) = sqrt((3-1)^2 + (4-8)^2) ~~ 4.47

"Change in distance "= 12.65 - 4.47 = 8.18

color(orange)(8.18 " is the reduction in the distance between A & B" color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"

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