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gladu [14]
3 years ago
12

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

Mathematics
2 answers:
riadik2000 [5.3K]3 years ago
4 0
The Answer is B hope this helps
MatroZZZ [7]3 years ago
3 0

Answer:

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 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=\sqrt{-1}.

Then,

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

x' = (-1-3i)\times 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.

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