Question 601037
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Actually, the third vertex can be in one of two places.  If the slope 2 line goes through (0,6) and the slope *[tex \Large -\frac{2}{3}] line goes through (0,0) you have one case.  If the lines are reversed you have another case.


Case 1:  slope 2 line through (0,6).  Equation of this line: *[tex \Large y\ =\ 2x\ +\ 6] (Slope-intercept form.)  Slope *[tex \Large -\frac{2}{3}] line through (0,0).  Equation of this line:  *[tex \Large y\ =\ -\frac{2}{3}x]


Solve the system of equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left{y\ =\ 2x\ +\ 6\cr y\ =\ -\frac{2}{3}x]


for the ordered pair *[tex \Large (x,\,y)] which is the point of intersection of the two lines.


The other case has the following system of equations:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left{y\ =\ 2x\cr y\ =\ -\frac{2}{3}x\ +\ 6]


{{{drawing(
500, 500, -5,5,-2,8,
grid(1),
graph(
500, 500, -5,5,-2,8,
2x+6,(-2/3)x,(-2/3)x+6,2x))}}}


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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