A segment with endpoints X Left parenthesis negative 6 comma 2 right parenthesis and Y Left parenthesis negative 1 comma negativ
e 3 right parenthesis is rotated 90º about the origin. What are the coordinates of X Prime and Y Prime? A. X prime Left parenthesis negative 1 comma negative 3 right parenthesis and Y prime Left parenthesis negative 6 comma 2 right parenthesis.
B. X prime Left parenthesis 2 comma 6 right parenthesis and Y prime Left parenthesis negative 3 comma 1 right parenthesis.
C. X prime Left parenthesis negative 2 comma negative 6 right parenthesis and Y prime Left parenthesis 3 comma negative 1 right parenthesis
D. X prime Left parenthesis 6 comma negative 2 right parenthesis and Y prime Left parenthesis 1 comma 3 right parenthesis
This can be done using complex numbers and its relations with plane geometry. The endpoints of the segment are X(-6,2) and Y(-1,-3). These points can be seen as complex numbers, just recall the geometric interpretation of complex numbers.
So, the complex counterpart of , and the complex counterpart of . Moreover, a rotation about the origin has an interpretation as multiplication by a complex number of modulus 1. In this particular case, a rotation of 90 degrees is equivalent to multiply by the complex unit: .
Then,
which gives the point
which gives the point .
The other option is to use a software to make geometrical constructions as Geogebra. Bellow there is an image attached made with Geogebra with the solution of the exercise.