Someone

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)

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.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.