SOMEONE PLEASE EXPLAIN!!

Four members of a marching band are arranged to form the vertices of a parallelogram. The coordinates of three of the band members are A(−3, 1), B(1, 3), and C(2, −1).

Part 1: Given this information, find all possible coordinates for the fourth band member.

Part 2: How do you know that you have found all possible coordinates? Justify your answer using words, mathematics, and/or patterns as needed.

To find if something is a parallelogram, they 1 set of line segments need to have the the slope. In this equation, Slope equals x1 + x2 divided by y1 + y2 (Or the other way around, x2 + x1 divided by y2 + y1)

[tex]m = \frac{( - 3 + 1)}{ ( 1 + 3)} = \frac{ - 2}{4} = - \frac{1}{2} [/tex]

For your other point, it could be (-4,5)

If this is confusing, please tell me! I'll try to better explain. It also helps to draw out a graph so you can plot the points.

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