# Point A is at (1 ,6 ) and point B is at (5 ,-3 ). 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(purple)(3.14 " is the reduction in the distance between A & B" color(orange)("due to the rotation of A by " pi " clockwise about the origin"

#### Explanation:

$A \left(1 , 6\right) , B \left(5 , - 3\right) , \text{ A rotated "pi " clockwise about origin}$

"To find change in distance of AB"

Using distance formula between two points,

$\overline{A B} = \sqrt{{\left(1 - 5\right)}^{2} + {\left(6 + 3\right)}^{2}} \approx 9.85$

$A \left(1 , 6\right) \to A ' \left(- 1 - 6\right) , \text{ as per rotation rule}$

$\overline{A ' B} = \sqrt{{\left(- 1 - 5\right)}^{2} + {\left(- 6 + 3\right)}^{2}} \approx 6.71$

$\text{Change in distance } = 9.85 - 6.71 = 3.14$

color(purple)(3.14 " is the reduction in the distance between A & B" color(orange)("due to the rotation of A by " pi " clockwise about the origin"#