Determine whether a figure with the given vertices is a parallelogram. use the method indicated. P(-5,1) S(-2,2) F(-1,-3) T(2,-2); Slope Formula

Answer 1

You need to make sure that the vertices form two pairs of lines, each pair having the same slope.

I'll assume the vertices are labeled PSFT in order. So, we want PS and FT to be parallel, and SF and TP to be parallel.

PS has slope (2-1)/(-2+5) = 1/3
FT has slope (-2+3)/(2+1) = 1/3

You can check the other pair.