Two of the sides of the triangle are perpendicular to each other, hence you can take the measure of either of those two sides and call it the base of the triangle and the other perpendicular side and call that the altitude of the triangle. A little work with the distance formula to find the measure of those two sides and then the old "base times height divided by 2" triangle area formula are all you need.
Step 1: Use the slope formula to find the slopes of the three sides.
where and are the coordinates of the given points.
Step 2: Once you have the three slopes, two of them will be negative reciprocals of each other, that is if one of the slopes is , then the other is . Those two sides are the two that are perpendicular.
Step 3: Calculate the measure of each of the two perpendicular sides using the distance formula:
Again, where and are the coordinates of the given points. Leave your answers in radical form.
Step 4: Multiply the two results from step 3 and then divide by 2 giving you the area of the specified triangle.
Let me know the answer you derived.
John
My calculator said it, I believe it, that settles it
