Question

Point A is at `(1 ,3 )` and point B is at `(2 ,-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?

Answer 1

`color(purple)(3.12 " 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 (1,3), B (2,-1), " A rotated "pi/2 " clockwise about origin"`

#"To find change in distance of AB"

Using distance formula between two points,

`bar(AB) = sqrt ((1-2)^2 + (3+1)^2) ~~ 4.12`

`A (1,3) to A'(3,-1), " as per rotation rule"`

`bar (A'B) = sqrt((3-2)^2 + (-1+1)^2) ~~ 1`

`"Change in distance "= 4.12 - 1 = 3.12`

`color(purple)(3.12 " is the change in the distance between A & B"` `color(purple)("due to the rotation of A by " (pi)/2 " clockwise about the origin"`