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stupidinmath

  • one year ago

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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  1. dpasingh
    • one year ago
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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.

  2. dpasingh
    • one year ago
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    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

  3. stupidinmath
    • one year ago
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    oh, got it, thank youuuu!

  4. dpasingh
    • one year ago
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    @stupidinmath welcome

  5. stupidinmath
    • one year ago
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    there's 2 answers?

  6. stupidinmath
    • one year ago
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    @dpasingh

  7. dpasingh
    • one year ago
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    Yes, exactly. there are two possible answer.

  8. stupidinmath
    • one year ago
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    oh okay

  9. dpasingh
    • one year ago
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    I fact there may be indefinite answers depending on the values we are assuming and second value obtaining accordingly...

  10. dpasingh
    • one year ago
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    sorry infinite answers

  11. stupidinmath
    • one year ago
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    i understand, thaanks a lot c:

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