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stupidinmath

  • 2 years 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
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    oh, got it, thank youuuu!

  4. dpasingh
    • 2 years ago
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    @stupidinmath welcome

  5. stupidinmath
    • 2 years ago
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    there's 2 answers?

  6. stupidinmath
    • 2 years ago
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    @dpasingh

  7. dpasingh
    • 2 years ago
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    Yes, exactly. there are two possible answer.

  8. stupidinmath
    • 2 years ago
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    oh okay

  9. dpasingh
    • 2 years 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
    • 2 years ago
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    sorry infinite answers

  11. stupidinmath
    • 2 years ago
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    i understand, thaanks a lot c:

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