Question

Determine whether the given coordinates are the vertices of a triangle. Explain. R(1, –4), S(–3, –20), T(5, 12) a. yes: RS + ST > RT, RS + RT > ST, RT + ST > RS c. no: RS + ST < RT b. no: RS + RT = ST d. yes: RS + ST < RT, RS + RT < ST, RT + ST < RS

Answer 1

Computing the distances involved will give the answer, but I might suggest a slightly different tack. Note that the slope of RS is the same as the slope of ST. This means the three points are collinear. Hard to be a triangle if all three points are in a line. It also generates the equality seen in answer b.