## 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)

1. dpasingh

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

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

oh, got it, thank youuuu!

4. dpasingh

@stupidinmath welcome

5. stupidinmath

6. stupidinmath

@dpasingh

7. dpasingh

Yes, exactly. there are two possible answer.

8. stupidinmath

oh okay

9. dpasingh

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

10. dpasingh