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stupidinmath

  • 10 months 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
    • 10 months 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
    • 10 months 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
    • 10 months ago
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    oh, got it, thank youuuu!

  4. dpasingh
    • 10 months ago
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    @stupidinmath welcome

  5. stupidinmath
    • 10 months ago
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    there's 2 answers?

  6. stupidinmath
    • 10 months ago
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    @dpasingh

  7. dpasingh
    • 10 months ago
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    Yes, exactly. there are two possible answer.

  8. stupidinmath
    • 10 months ago
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    oh okay

  9. dpasingh
    • 10 months 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
    • 10 months ago
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    sorry infinite answers

  11. stupidinmath
    • 10 months ago
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    i understand, thaanks a lot c:

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