# Point A is at (1 ,-9 ) and point B is at (-2 ,8 ). 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?

The new point A will be at $\left(9 , 1\right)$
Difference in distance $= \sqrt{298} - \sqrt{170} = 13.0384 \text{ }$units

#### Explanation:

The old distance between $A$ and $B$ is

distance $d = \sqrt{{\left({x}_{a} - {x}_{b}\right)}^{2} + {\left({y}_{a} - {y}_{b}\right)}^{2}}$

$d = \sqrt{{\left(1 - - 2\right)}^{2} + {\left(- 9 - 8\right)}^{2}}$

$d = \sqrt{{\left(3\right)}^{2} + {\left(- 17\right)}^{2}}$

$d = \sqrt{9 + 289}$

$d = \sqrt{298}$

The new distance between $A$ and $B$ is

distance $d = \sqrt{{\left({x}_{a} - {x}_{b}\right)}^{2} + {\left({y}_{a} - {y}_{b}\right)}^{2}}$

$d = \sqrt{{\left(9 - - 2\right)}^{2} + {\left(1 - 8\right)}^{2}}$

$d = \sqrt{{\left(11\right)}^{2} + {\left(- 7\right)}^{2}}$

$d = \sqrt{121 + 49}$

$d = \sqrt{170}$

Difference in distance $= \sqrt{298} - \sqrt{170} = 13.0384 \text{ }$units