posted by Lily on .
Write a system of inequalities to express the exterior of the triangle ABD if A=(-2,7), B=(4,0), and C=(1,-3).
Derive equations for the three lines connecting the three points. Then change the equations to inequalities to represent the region on the side of the lines that is outside the triangle.
It will help if you draw the three points on graph paper and connect them with extended lines passing through pairs of points.
Example: The line connecting A and B has slope m = (7-0)/(-2-4) = -7/6 and the equation for this line, extended to infinity, is
(y-7) = (-7/6) (x+2) or
y = -7x/6 -7/3 + 7 = -7x/6 +14/3
The region above this line is outside the triangle, so one of the inequalities is
y > -7x/6 +14/3