Question

Point A is at `(-3 ,-4 )` and point B is at `(1 ,8 )`. 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

`color(orange)(8.18 " is the reduction in the distance between A & B"` `color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"`

Explanation:

`A (-3, -4), B (1, 8), " A rotated "pi " clockwise about origin"`

#"To find change in distance of AB"

Using distance formula between two points,

`bar(AB) = sqrt ((-3 -1)^2 + (-4 - 8)^2) ~~ 12.65`

`A (-3, -4) to A'(3, 4), " as per rotation rule"`

`bar (A'B) = sqrt((3-1)^2 + (4-8)^2) ~~ 4.47`

`"Change in distance "= 12.65 - 4.47 = 8.18`

`color(orange)(8.18 " is the reduction in the distance between A & B"` `color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"`