Asegment with endpoints x left parenthesis negative 6 comma 2 right parenthesis and y left parenthesis negative 1 comma negative 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

The correct answer is C.

Step-by-step explanation:

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.

1     sepan

2     encuentren

3     tenga

4     hable

5   parezca

6   llegue