Point A is at $(6, 2)$ $(6 ,2 )$ and point B is at $(3, 8)$ $(3 ,8 )$ . Point A is rotated $\frac{3 π}{2}$ $(3pi)/2$ 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?

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Point A is at $(6, 2)$ $(6 ,2 )$ and point B is at $(3, 8)$ $(3 ,8 )$ . Point A is rotated $\frac{3 π}{2}$ $(3pi)/2$ 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?

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Answer 1 · 2018-02-07T16:15:12

(-2,6) is the new coordinate of Point A
Now, the points are closer by 1.323

Explanation:

Origin $(0, 0)$ $(0,0)$
Point A $(6, 2)$ $(6,2)$
Point B $(3, 8)$ $(3,8)$

Distance between points A and B is
$\sqrt{{(8 - 2)}^{2} + {(3 - 6)}^{2}}$ $sqrt((8-2)^2+(3-6)^2$
$= \sqrt{6^{2} + 3^{2}}$ $=sqrt(6^2+3^2$
$= \sqrt{36 + 9}$ $=sqrt(36+9$
$= \sqrt{45}$ $=sqrt(45)$
$= 6.708$ $=6.708$

After transformation
Rotation by $\frac{3 π}{2}$ $(3pi)/2$
When rotated by $\frac{π}{2}$ $pi/2$
the new coordinates are $(2, - 6)$ $(2,-6)$
When further rotated by $π$ $pi$
the coordinates are further transformed into $- 2, 6)$ $-2,6)$
$(- 2, 6)$ $(-2,6)$ is the transformed coordinate of the point A

After transformation
Point A $(- 2, 6)$ $(-2,6)$
Point B $(3, 8)$ $(3,8)$

Distance after transformation is
$\sqrt{{(8 - 6)}^{2} + {(3 - (- 2))}^{2}}$ $sqrt((8-6)^2+(3-(-2))^2$
$= \sqrt{2^{2} + 5^{2}}$ $=sqrt(2^2+5^2$
$= \sqrt{4 + 25}$ $=sqrt(4+25$
$= \sqrt{29}$ $=sqrt(29)$
$= 5.385$ $=5.385$

The distance between the points A and B has changed by
$5.385 - 6.708 = - 1.323$ $5.385-6.708=-1.323$

Now, the points are closer by 1.323

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Point A is at $(6, 2)$ $(6 ,2 )$ and point B is at $(3, 8)$ $(3 ,8 )$ . Point A is rotated $\frac{3 π}{2}$ $(3pi)/2$ 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

Explanation:

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Science

Math

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Point A is at (6,2)(6 ,2 ) and point B is at (3,8)(3 ,8 ). Point A is rotated 3π2(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

Explanation:

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Impact of this question

Point A is at $(6, 2)$ $(6 ,2 )$ and point B is at $(3, 8)$ $(3 ,8 )$ . Point A is rotated $\frac{3 π}{2}$ $(3pi)/2$ 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?