58. Three line segments are graphed in the standard (x, y) coordinate plane below. Line segment AB has endpoints A(2,0) and B(4,0), A'B' is the image of AB after a rotation counterclockwise () by 120° about the origin, and A"B" is A'B' projected onto the x-axis. What is the length, in coordinate units, of A"B" ?

Answer and Explanation

Your Answer is

Correct Answer is F

Explanation

First pass through point A' and draw a vertical line from B'B'' to intersect B'B'' at D. In this right triangle, we know that ∠ DA'B'=180o-120o=60o, A'B' length and AB Equal to 2. So the length of A'D is 2×cos60o=1

It is easy to prove quadrilateral A'A''B'' ;D is a rectangle, then the length of A''B'' is 1