Question

Point A is at `(-9 ,7 )` and point B is at `(2 ,1 )`. 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(blue)("New coordinates of point A due to rotation "(9,-7)`

`color(brown)("Reduction in distance due to rotation of point A by " pi^c`

`color(crimson)(bar (AB) - bar (A'B) = 12.53 - 10.63 = 1.9`

Explanation:

`A (-9,7), B (2,1)," Point A rotated clockwise by p" pi^c`

`A'(x,y) = A'(9,-7)`

`"Distance " = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)`

`bar(AB) = sqrt((-9-2)^2 + (7-1)^2) = 12.53`

`bar(A'B) = sqrt((9-2)^2 + (-7-1)^2) = 10.63`

`color(brown)("Reduction in distance due to rotation of point A by " pi^c`

`color(crimson)(bar (AB) - bar (A'B) = 12.53 - 10.63 = 1.9`