Point A is at $(-7 ,3 )$ and point B is at $(5 ,4 )$ . 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?

Question

1759 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-02T00:12:24

$A' = (7, -3)$
The distance has decreased by $sqrt(145) - sqrt(53) ~~ 4.76$

Given: $A(-7, 3), B(5, 4)$ Point $A$ is rotated $pi$ clockwise about the origin.

A $pi$ rotation clockwise is a $180^@$ rotation CW.

The coordinate rule for a $180^@$ rotation CW is: $(x, y) -> (-x, -y)$

Using the coordinate rule: $A' = (7, -3)$
enter image source here

The distance formula is $d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)$

$d_(AB) = sqrt((5 - -7)^2 + (4 - 3)^2) = sqrt(12^2 + 1^2) = sqrt(145)$

$d_(A'B) = sqrt((5-7)^2 + (4 - -3)^2) = sqrt(2^2 + 7^2) = sqrt(53)$

The distance between point $A$ and $B$ has not changed.

The distance between the rotated point $A$ = $A'$ and $B$ is $sqrt(145) - sqrt(53) ~~4.76$

Point A is at (-7 ,3 )(-7 ,3 ) and point B is at (5 ,4 )(5 ,4 ). Point A is rotated pi 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?