# Point A is at (-3 ,8 ) and point B is at (-7 ,-5 ). Point A is rotated pi/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?

Feb 11, 2018

$\left(8 , 3\right) , \approx 3.40$

#### Explanation:

$\text{under a clockwise rotation about the origin of } \frac{\pi}{2}$

• " a point "(x,y)to(y,-x)

$\Rightarrow A \left(- 3 , 8\right) \to A ' \left(8 , 3\right) \text{where A' is the image of A}$

$\text{to calculate the distance use the "color(blue)"distance formula}$

•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

$\text{let "(x_1,y_1)=A(-3,8)" and } \left({x}_{2} , {y}_{2}\right) = B \left(- 7 , - 5\right)$

$A B = \sqrt{{\left(- 7 + 3\right)}^{2} + {\left(- 5 - 8\right)}^{2}} = \sqrt{16 + 169} = \sqrt{185}$

$\text{let(x_1,y_1)=A'(8,3)" and } \left({x}_{2} , {y}_{2}\right) = B \left(- 7 , - 5\right)$

$A ' B = \sqrt{{\left(- 7 - 8\right)}^{2} + {\left(- 5 - 3\right)}^{2}} = \sqrt{225 + 64} = 17$

$\text{change in distance } = 17 - \sqrt{185} \approx 3.40$