Question

A segment 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

Answer 1

The Answer is B hope this helps

Answer 2

The correct answer is C.

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
`X(-6,2) is x=-6+2i`, and the complex counterpart of
`Y(-1,-3) = -1-3i`. 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:
`i=√(-1)`.

Then,

`x' = (-6+2i)* i = -2-6i` which gives the point
`X'(-2,-6)`

`x' = (-1-3i)* i = 3-1i` which gives the point
`Y'(2,-1)`.

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.