Point A is at #(-5 ,9 )# and point B is at #(-1 ,7 )#. 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?

Question

1361 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-06T10:06:19

New coordinates of A (-9, -5) & the distance changed (increase) = 9.95 units

enter image source here

A(-5,9), B(-1,7)

With clockwise rotation by #(3pi)/2# around the origin

Point A moves from III quadrant to IV quadrant.

# (x,y) -> (-y,x)#

#A(-5,9) -> A' (-9, -5)#

Using distance formula,

#vec(AB) = sqrt(-5 - (-1))^2 + (9-7)^2) = sqrt20#

#vec(AB') = sqrt((-9-(-1))^2 + ((-5)-7)^2) = sqrt208#

#A'B - AB = sqrt208 - sqrt20 = 9.95# units