how do you find the equation for the line containg the side opposite the side containg the first two vertices?
To find the equation for the line containing the side opposite the side containing the first two vertices of a triangle, you will need the coordinates of the three vertices. Let's assume the first two vertices are (x1, y1) and (x2, y2), and the third vertex is (x3, y3).
1. First, find the slope (m) of the line containing the side connecting the first two vertices. The slope can be calculated as:
m = (y2 - y1) / (x2 - x1)
2. Next, find the equation for the line by using the point-slope form, y - y1 = m(x - x1). Choose any of the two given points. For example, if you use (x1, y1), the equation becomes:
y - y1 = m(x - x1)
3. Finally, substitute the coordinates of the third vertex (x3, y3) into the equation to check if the third vertex lies on the line. If the equation is satisfied, then the line contains the side opposite the side containing the first two vertices.
Note: If the third vertex lies on the line, you don't need to proceed further. If it doesn't lie on the line, then the equation you found won't represent the line containing the side opposite the side connecting the first two vertices.