# Point A is at (4 ,-8 ) and point B is at (-1 ,-2 ). 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?

##### 1 Answer
Mar 20, 2018

Increase in distance due to rotation of point A (4,-8) about origin by $\frac{3 \pi}{2}$ clockwise is

color(indigo)(vec(A'B) - vec (AB) = sqrt117 - sqrt61 = 3

#### Explanation:

$\text{Point " A (4,-8), "Point } B \left(- 1 , - 2\right)$

Point A rotated about origin by $\frac{3 \pi}{2}$ clockwise.

Using distance frmula,

$\vec{A B} = \sqrt{{\left(4 + 1\right)}^{2} + {\left(- 8 + 2\right)}^{2}} = \sqrt{61}$

$A \left(4 , - 8\right) - > A ' \left(8 , 4\right) , \text{ (from quadrant IV to quadrant I)}$

$\vec{A ' B} = \sqrt{{\left(8 + 1\right)}^{2} + {\left(4 + 2\right)}^{2}} = \sqrt{117}$

Increase in distance due to rotation of point A (4,-8) about origin by $\frac{3 \pi}{2}$ clockwise is

color(indigo)(vec(A'B) - vec (AB) = sqrt117 - sqrt61 = 3