# Point A is at (-3 ,-4 ) and point B is at (1 ,8 ). 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?

Jun 30, 2018

color(orange)(8.18 " is the reduction in the distance between A & B" color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"

#### Explanation:

$A \left(- 3 , - 4\right) , B \left(1 , 8\right) , \text{ A rotated "pi " clockwise about origin}$

"To find change in distance of AB"

Using distance formula between two points,

$\overline{A B} = \sqrt{{\left(- 3 - 1\right)}^{2} + {\left(- 4 - 8\right)}^{2}} \approx 12.65$

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

$\overline{A ' B} = \sqrt{{\left(3 - 1\right)}^{2} + {\left(4 - 8\right)}^{2}} \approx 4.47$

$\text{Change in distance } = 12.65 - 4.47 = 8.18$

color(orange)(8.18 " is the reduction in the distance between A & B" color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"#