Question

Point A is at `(2 ,-1 )` and point B is at `(9 ,-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?

Answer 1

As below

Explanation:

`A (2,-1), B (9, -7), " A rotated "(3pi)/2 " clockwise about origin"`

#"To find change in distance of AB"

Using distance formula between two points,

`bar(AB) = sqrt ((2-9)^2 + (-1 + 7)^2) ~~ 9.22`

`A (2, -1) to A'(1, 2), " as per rotation rule"`

`bar (A'B) = sqrt((1-9)^2 + (2+7)^2) = 12.04`

`"Change in distance "= 12.04 - 9.22 = 2.82`

`color(blue)(2.82 " is the change in the distance between A & B"` `color(crimson)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"`