Question

Point A is at `(4 ,-2 )` and point B is at `(5 ,-4 )`. 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

`color(violet)(0.76 " is the change in the distance between A & B"` `color(violet)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"`

Explanation:

`A (4, -2), B (5, -4), " A rotated "(3pi)/2 " clockwise about origin"`

#"To find change in distance of AB"

Using distance formula between two points,

`bar(AB) = sqrt ((4-5)^2 + (-2 + 4)^2) ~~ 2.24`

`A (4, -2) to A'(2, -4), " as per rotation rule"`

`bar (A'B) = sqrt((2-5)^2 + (-4+4)^2) = 3`

`"Change in distance "= 3 - 2.24 = 0.76`

`color(violet)(0.76 " is the change in the distance between A & B"` `color(violet)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"`