The points (0,0) and (-2,2) are two vertices of an equilateral triangle. Which of the following could be the coordinates of the third vertex? a. (-2,0) b. (-0.73,2.73) c. (-0.73,0.73) d. (0,2) e. (0.73,0.73)

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The points (0,0) and (-2,2) are two vertices of an equilateral triangle. Which of the following could be the coordinates of the third vertex? a. (-2,0) b. (-0.73,2.73) c. (-0.73,0.73) d. (0,2) e. (0.73,0.73)

Mathematics
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Since given is the equilateral triangle whose all the vertices are at equidistance. Let the coordinates of the third vertex be (x, y) Hence distance of (x, y) from (0, 0) = distance of (x, y) from (-2, 2) therefore by distance formula we have \[(x-0)^2+(y-0)^2 = [x-(-2)]^2+(y-2)^2\] \[\rightarrow x^2+y^2 = [x+2]^2+(y-2)^2\] \[\rightarrow x^2+y^2 = x^2 +4 + 4x + y^2+4- 4y\] \[\rightarrow 0 =8 + 4x - 4y\] \[\rightarrow 4y -4x =8 \rightarrow y -x =2 \] now cosider x=0 we get y-0= 2 i.e. y=2 hence (x, y) = (0, 2) could be the coordinates of the third vertex.
now cosider y=0 we get 0-x= 2 i.e.- x=2 i.e. x=-2 hence (x, y) = (-2, 0) could also be the coordinates of the third vertex
oh, got it, thank youuuu!

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Other answers:

there's 2 answers?
Yes, exactly. there are two possible answer.
oh okay
I fact there may be indefinite answers depending on the values we are assuming and second value obtaining accordingly...
sorry infinite answers
i understand, thaanks a lot c:

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