Point A is at $(-9 ,7 )$ and point B is at $(2 ,1 )$ . 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

2446 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-12T02:42:17

$color(blue)("New coordinates of point A due to rotation "(9,-7)$

$color(brown)("Reduction in distance due to rotation of point A by " pi^c$

$color(crimson)(bar (AB) - bar (A'B) = 12.53 - 10.63 = 1.9$

$A (-9,7), B (2,1)," Point A rotated clockwise by p" pi^c$

![https://teacher.desmos.com/activitybuilder/custom/566b16af914c731d06ef1953]( useruploads.socratic.org )

$A'(x,y) = A'(9,-7)$

$"Distance " = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)$

$bar(AB) = sqrt((-9-2)^2 + (7-1)^2) = 12.53$

$bar(A'B) = sqrt((9-2)^2 + (-7-1)^2) = 10.63$

$color(brown)("Reduction in distance due to rotation of point A by " pi^c$

$color(crimson)(bar (AB) - bar (A'B) = 12.53 - 10.63 = 1.9$

Point A is at (-9 ,7 )(-9 ,7 ) and point B is at (2 ,1 )(2 ,1 ). 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?