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Point A is at (-2 ,-4 ) and point B is at (-3 ,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?

Mar 20, 2018

Increase in distance due to the rotation of point A is

color(green)(vec(A'B) - vec(AB) = sqrt74 - sqrt50 = 1.53

Explanation:

$\text{Point " A (-2, -4), "Point } B \left(- 3 , 3\right)$

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

To find change in distance between Ab due to rotation of point A.

$A \left(- 2 , - 4\right) \to A ' \left(4 , - 2\right) , \text{ shifted from III to IV quadrant}$

Using distance formula,

$\vec{A B} = \sqrt{{\left(- 2 + 3\right)}^{2} + {\left(- 4 - 3\right)}^{2}} = \sqrt{50}$

$\vec{A ' B} = \sqrt{{\left(4 + 3\right)}^{2} + {\left(- 2 - 3\right)}^{2}} = \sqrt{74}$

Increase in distance due to the rotation of point A is

color(green)(vec(A'B) - vec(AB) = sqrt74 - sqrt50 = 1.53