Question

Point A is at `(5 ,3 )` and point B is at `(-3 ,2 )`. 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?

Answer 1

`color(purple)(1.16 " is the change in the distance between A & B"` `color(orange)("due to the rotation of A by " (pi)/2 " clockwise about the origin"`

Explanation:

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

#"To find change in distance of AB"

Using distance formula between two points,

`bar(AB) = sqrt ((5+3)^2 + (3-2)^2) ~~ 8.06`

`A (5,3) to A'(3,-5), " as per rotation rule"`

`bar (A'B) = sqrt((3+3)^2 + (-5-2)^2) ~~ 9.22`

`"Change in distance "= 9.22 - 8.06 = 1.16`

`color(purple)(1.16 " is the change in the distance between A & B"` `color(orange)("due to the rotation of A by " (pi)/2 " clockwise about the origin"`