A vector from the origin to terminal point )2,3) is shown in the standard (x,y) coordinate plane below. The vector will be rotated counterclockwise by 90 degrees about the origin, resulting in a new vector. What will be the coordinates of the terminal point of the new vector?

I thought that the new point would be (-2,3), since the point moved from the 1st to the 3rd quadrant. The answer is (-3,2) and I'm confused D:

thanks!

Question

A vector from the origin to terminal point )2,3) is shown in the standard (x,y) coordinate plane below. The vector will be rotated counterclockwise by 90 degrees about the origin, resulting in a new vector. What will be the coordinates of the terminal point of the new vector?

I thought that the new point would be (-2,3), since the point moved from the 1st to the 3rd quadrant. The answer is (-3,2) and I'm confused D:

thanks!

anonymous · Answer

@kirbykirby  help again? :)

kirbykirby · Answer

Ok well let's maybe do a drawing to see what's going on:

kirbykirby · Answer

|dw:1410482663106:dw|

anonymous · Answer

so does it have something to do with the slope being negative?

kirbykirby · Answer

Well one way I though about it.. was to determine the length of the hypotenuse using pythagoras: $\sqrt{3^2+2^2}$ and then use trig (like using sine or cosine) to figure out the angle formed by the triangle with the x-axis. Then, using the fact that you rotated 90 degrees, you can find the new angle formed by the triangle once it has rotated. The length of the hypotenuse doesn't change by a rotation, so then you can use trig again to find the new lengths of the sides of your triangle. 

Although I am pretty sure there is some "theorem" or result that quickly gives you the result of the coordinates after some rotation immediately. But I don't remember it so I just go using basic results lol.