# Point A is at (-9 ,-6 ) and point B is at (-2 ,-7 ). 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?

Jun 30, 2018

color(brown)(8.23" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"

#### Explanation:

$A \left(- 9 , - 6\right) , B \left(- 2 , - 7\right) , \text{ A rotated (3pi)/2 clockwise about origin}$

"To find change in distance of AB"

Using distance formula between two points,

$\overline{A B} = \sqrt{{\left(- 9 + 2\right)}^{2} + {\left(- 6 + 7\right)}^{2}} = 7.07$

$A \left(- 9 , - 6\right) \to A ' \left(6 , - 9\right) , \text{ as per rotation rule}$

$\overline{A ' B} = \sqrt{{\left(- 9 - 6\right)}^{2} + {\left(- 6 + 9\right)}^{2}} \approx 15.3$

$\text{Change in distance } = 15.3 - 7.07 = 8.23$

color(brown)(8.23" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"#