# 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?

May 12, 2018

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:

$A \left(- 9 , 7\right) , B \left(2 , 1\right) , \text{ Point A rotated clockwise by p} {\pi}^{c}$

$A ' \left(x , y\right) = A ' \left(9 , - 7\right)$

$\text{Distance } = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

$\overline{A B} = \sqrt{{\left(- 9 - 2\right)}^{2} + {\left(7 - 1\right)}^{2}} = 12.53$

$\overline{A ' B} = \sqrt{{\left(9 - 2\right)}^{2} + {\left(- 7 - 1\right)}^{2}} = 10.63$

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