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Point A is at #(-5 ,9 )# and point B is at #(-3 ,4 )#. Point A is rotated #(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?

Answer 1

Evelyn Arboleda

#color(indigo)("Increase in distance due to the rotation of A is "#

#color(purple)(= vec(A'B) - vec(AB) = 6.08 - 5.39 = 0.69 " units"#

#A(-5,9), B (-3,4)#

#vec(AB) = sqrt((-5+3)^2 + (9-4)^2) = 5.39 " units"#

Point A rotated #(3pi)/2# clockwise about the origin.

#A(-5, 9) -> A'(-9, 5)#

#vec(A'B) sqrt((-9+3)^2 + (5-4)^2) = 6.08 " units#

#color(indigo)("Increase in distance due to the rotation of A is "#

#color(purple)(= vec(A'B) - vec(AB) = 6.08 - 5.39 = 0.69 " units"#

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Answer 2

Allison Allen

The new coordinates of point A after rotating clockwise about the origin by ( \frac{3\pi}{2} ) radians are (9, 5). The distance between points A and B has changed by ( \sqrt{(9 - (-3))^2 + (5 - 4)^2} - \sqrt{(-5 - (-3))^2 + (9 - 4)^2} ) units.

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Answer from HIX Tutor

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