Question

Point A is at `(-2 ,5 )` and point B is at `(-3 ,3 )`. Point A is rotated `pi` 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, 5), B (-3, 3), " A rotated " pi " clockwise about origin"`

#"To find change in distance of AB"

Using distance formula between two points,

`bar(AB) = sqrt ((-2+ 3)^2 + (5 - 3)^2) ~~ 2.2361`

`A (-2, 5) to A'(2, -5), " as per rotation rule"`

`bar (A'B) = sqrt((2 + 3)^2 + (-5 - 3)^2) = 9.434`

`"Change in distance "= 9.434 - 2.2361 = 7.198`

`color(blue)(7.198 " is the change in the distance between A & B"` `color(crimson)("due to the rotation of A by " pi " clockwise about the origin"`