Question

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)

Answer 1

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.

Answer 2

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

Answer 3

oh, got it, thank youuuu!

Answer 4

@stupidinmath welcome

Answer 5

there's 2 answers?

Answer 6

@dpasingh

Answer 7

Yes, exactly. there are two possible answer.

Answer 8

oh okay

Answer 9

I fact there may be indefinite answers depending on the values we are assuming and second value obtaining accordingly...

Answer 10

sorry infinite answers

Answer 11

i understand, thaanks a lot c: