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?

1 Answer
Jim G.
Feb 11, 2018

(8,3),~~3.40

Explanation:

"under a clockwise rotation about the origin of "pi/2

• " a point "(x,y)to(y,-x)

rArrA(-3,8)toA'(8,3)"where A' is the image of A"

"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)

"let "(x_1,y_1)=A(-3,8)" and "(x_2,y_2)=B(-7,-5)

AB=sqrt((-7+3)^2+(-5-8)^2)=sqrt(16+169)=sqrt185

"let(x_1,y_1)=A'(8,3)" and "(x_2,y_2)=B(-7,-5)

A'B=sqrt((-7-8)^2+(-5-3)^2)=sqrt(225+64)=17

"change in distance "=17-sqrt185~~3.40

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