Point A is at (4 ,-8 ) and point B is at (-1 ,-2 ). 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
Mar 20, 2018

Increase in distance due to rotation of point A (4,-8) about origin by (3pi)/2 clockwise is

color(indigo)(vec(A'B) - vec (AB) = sqrt117 - sqrt61 = 3

Explanation:

"Point " A (4,-8), "Point "B(-1,-2)

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

Using distance frmula,

vec(AB) = sqrt((4+1)^2 + (-8+2)^2) = sqrt61

http://www.math-only-math.com/signs-of-coordinates.htmlhttp://www.math-only-math.com/signs-of-coordinates.html
A (4, -8) - > A'(8,4), " (from quadrant IV to quadrant I)"

vec(A'B) = sqrt((8+1)^2 + (4 + 2)^2) = sqrt117

Increase in distance due to rotation of point A (4,-8) about origin by (3pi)/2 clockwise is

color(indigo)(vec(A'B) - vec (AB) = sqrt117 - sqrt61 = 3