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jmc

geometry intermediate

Problem

Two vertices of an obtuse triangle are and . The third vertex is located on the negative branch of the -axis. What are the coordinates of the third vertex if the area of the triangle is 30 square units?
Solution
We know that, for a triangle, area = 1/2(base)(height), which equals 30 in this problem. We also know that the height of the triangle is 4 if we use the horizontal leg on the x-axis as the base. Now we can plug this information into the equation to find the length of the base that runs along the x-axis. The equation is , so . Since the 3rd vertex is on the x-axis we know that it extends straight left 15 units from the vertex at (0, 0), bringing us to the point .
Final answer
(-15, 0)