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

To determine whether a figure with the given vertices is a parallelogram, we can use the Slope Formula.

The Slope Formula is a mathematical formula used to calculate the slope of a line between two points on a coordinate plane. It is given by:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Let's find the slopes of the two pairs of opposite sides of the figure:

1) Slope of PS:
mPS = (y2 - y1) / (x2 - x1) = (2 - 1) / (-2 - (-5)) = 1 / 3

2) Slope of FT:
mFT = (y2 - y1) / (x2 - x1) = (-2 - (-3)) / (2 - (-1)) = 1 / 3

If the slopes of the opposite sides of a figure are equal, then the figure is a parallelogram.

In our case, the slopes of PS and FT are both 1/3. Therefore, the figure with the given vertices (P, S, F, T) is a parallelogram.

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.