How to determine point is Inside the Triangle?

In the xy-plane, point R (2,3) and point S (5,6) are two vertices of triangle RST. If the sum of the slopes...?

• In the xy-plane, point R (2,3) and point S (5,6) are two vertices of triangle RST. If the sum of the slopes of the sides of the triangle is 1, which of the following angles could be a right angle? I. R II. S III. T A. None B. I only C. III only D. I and II only E. I, II, and III I think it's C, because the slope of RS is already 1, but if point T was at (5,3), this would form a right triangle with the hypotenuse having the slope of one and the other two legs would have a slope of undefined and 0. Disregarding the undefined, this would add up to 1. However, my book says the answer is none. Am I right or am I right on this one?

• Answer:

  Sorry, you can't just disregard the undefined slope. Sometimes the slope is also called ∞. You are correct that T can't have a right angle. That leaves R and S as possibilities. If you put a right angle at either R or S you will have a side with slope -1. So the first two slopes add to 1 - 1 = 0. That means the third side would have to have a slope of 1. But that would make the third side parallel to RS and triangles can't have two parallel sides. So the answer is None. A. None.