Question

Point A is at `(1 ,3 )` and point B is at `(2 ,6 )`. 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(maroon)("Increase in distance due to the rotation is "`

`color(crimson)(vec(A'B) - vec(AB) = 7.07 - 3.16 = 3.9 " units"`

Explanation:

Given ": `A (1,3), B (2,6), "Point A rotated by " pi/2 " clockwise about the origin"`

`vec (AB) = sqrt((1-2)^2 + (3-6)^2) = 3.16 " units"`

`A (1,3) -> A' (3, -1)`

`vec(A'B) = sqrt((3-2)^2 + (-1-6)^2) = 7.07 " units"`

`color(maroon)("Increase in distance due to the rotation is "`

`color(crimson)(vec(A'B) - vec(AB) = 7.07 - 3.16 = 3.9 " units"`