## 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) 5 months ago 5 months ago

1. dpasingh Group Title

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 Group Title

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 Group Title

oh, got it, thank youuuu!

4. dpasingh Group Title

@stupidinmath welcome

5. stupidinmath Group Title

6. stupidinmath Group Title

@dpasingh

7. dpasingh Group Title

Yes, exactly. there are two possible answer.

8. stupidinmath Group Title

oh okay

9. dpasingh Group Title

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

10. dpasingh Group Title