The graphs of 3x+2y=1, y=2, and 3x-4y=-29 contain the sides of a triangle. Find the measure of the area of the triangle.
Hint:
The three lines are not parallel, as can be checked from the slopes, so they intersect each other at three different points, which are the vertices of the the triangle.
Solve for the three points, for example,
y=2
3x+2y=1
gives
3x+2(2)=1
x=(1-4)/3=-1
so (-1,2)=(x1,y1) is one of the vertices.
Find the other two vertices (x2,y2), (x3,y3).
The area is given by
A=|(x1*y2+x2*y3+x3*y1-x2*y1-x3*y2-x3*y1)|/2
The sign |...| means absolute value, take only the positive values between the two bars.
Re