# Point A is at (5 ,7 ) and point B is at (-6 ,-3 ). 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?

Apr 8, 2018

color(brown)("There is no change in the distance between A & B due to the rotation of " (3pi)/2 " clockwise about the origin"

#### Explanation:

$A \left(5 , 7\right) , B \left(- 6 , - 3\right) , \text{ A rotated (3pi)/2 clockwise about origin}$

"To find change in distance of AB"

Using distance formula between two points,

$\overline{A B} = \sqrt{{\left(5 + 6\right)}^{2} + {\left(7 + 3\right)}^{2}} = 14.87$

$A \left(5 , 7\right) \to A ' \left(- 7 , 5\right) , \text{ as per rotation rule}$

$B \left(- 6 , - 3\right) \to B ' \left(3 , - 6\right) , \text{ as per rotation rule}$

$\overline{A ' B '} = \sqrt{{\left(- 7 - 3\right)}^{2} + {\left(5 + 6\right)}^{2}} = 14.87$

color(brown)("There is no change in the distance between A & B due to the rotation of " (3pi)/2 " clockwise about the origin"#