Point A is at (-1 ,-4 ) and point B is at (-3 ,-1 ). Point A is rotated pi/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
Mar 20, 2018

Decrease in distance due to the rotation of A about origin by (pi/2) clockwise is

color(red)(vec(AB) - vec(A'B) = sqrt13 - sqrt5 = 1.3695

Explanation:

![https://www.flexiprep.com/NCERT-Exercise-Solutions/Mathematics/Class-9/Ch-3-Coordinate-Geometry-Exercise-3-3-Solutions.html](useruploads.socratic.org)

"Point " A(-1, -4), "Point " B (-3, 1)

Point A rotated about origin by pi/2 clockwise.

A (-1, -4) -> A' (-4, 1), " from III to II quadrant"

Using distance formula between two points,

vec(AB) = sqrt((-1+3)^2 + (-4 + 1)^2 ) = sqrt13

vec (A'B) = sqrt((-4+3)^2 + (1 + 1)^2) = sqrt5

Decrease in distance due to the rotation of A about origin by (pi/2) clockwise is

color(red)(vec(AB) - vec(A'B) = sqrt13 - sqrt5 = 1.3695

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