Point A is at (-3 ,-4 ) and point B is at (-5 ,-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?

Jun 30, 2018

color(cyan)(5.83 " is the change in the distance between A & B" color(cyan)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"

Explanation:

$A \left(- 3 , - 4\right) , B \left(- 5 , - 8\right) , \text{ A rotated "(3pi)/2 " clockwise about origin}$

"To find change in distance of AB"

Using distance formula between two points,

$\overline{A B} = \sqrt{{\left(- 3 + 5\right)}^{2} + {\left(- 4 + 8\right)}^{2}} \approx 4.47$

$A \left(- 3 , - 4\right) \to A ' \left(4 , - 3\right) , \text{ as per rotation rule}$

$\overline{A ' B} = \sqrt{{\left(4 + 5\right)}^{2} + {\left(- 3 + 8\right)}^{2}} \approx 10.3$

$\text{Change in distance } = 10.3 - 4.47 = 5.83$

color(cyan)(5.83 " is the change in the distance between A & B" color(cyan)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"#