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stupidinmath Group Title

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)

  • 6 months ago
  • 6 months ago

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  1. dpasingh Group Title
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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.

    • 6 months ago
  2. dpasingh Group Title
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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

    • 6 months ago
  3. stupidinmath Group Title
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    oh, got it, thank youuuu!

    • 6 months ago
  4. dpasingh Group Title
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    @stupidinmath welcome

    • 6 months ago
  5. stupidinmath Group Title
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    there's 2 answers?

    • 6 months ago
  6. stupidinmath Group Title
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    @dpasingh

    • 6 months ago
  7. dpasingh Group Title
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    Yes, exactly. there are two possible answer.

    • 6 months ago
  8. stupidinmath Group Title
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    oh okay

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

    • 6 months ago
  10. dpasingh Group Title
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    sorry infinite answers

    • 6 months ago
  11. stupidinmath Group Title
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    i understand, thaanks a lot c:

    • 6 months ago
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