Question

Point A is at `(1 ,6 )` and point B is at `(5 ,-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

`color(purple)(3.14 " is the reduction in the distance between A & B"` `color(orange)("due to the rotation of A by " pi " clockwise about the origin"`

Explanation:

`A (1, 6), B (5, -3), " A rotated "pi " clockwise about origin"`

#"To find change in distance of AB"

Using distance formula between two points,

`bar(AB) = sqrt ((1-5)^2 + (6+3)^2) ~~ 9.85`

`A (1, 6) to A'(-1 - 6), " as per rotation rule"`

`bar (A'B) = sqrt((-1-5)^2 + (-6+3)^2) ~~ 6.71`

`"Change in distance "= 9.85 - 6.71 = 3.14`

`color(purple)(3.14 " is the reduction in the distance between A & B"` `color(orange)("due to the rotation of A by " pi " clockwise about the origin"`