SOLUTION:
We are given the points;
[tex]A(4,-7),B(1,1),C(-5,-4)[/tex]
We need the coordinates of D such that A, B, C, and D would form a parallelogram.
A key idea is that in a parallelogram, the distance between coordinates that make up the parallels are equal.
Here is a graph of the points;
Now, we can find D;
[tex]\begin{gathered} (1--5,1--4)+(4,-7) \\ (6,5)+(4,-7) \\ (10,-2) \end{gathered}[/tex]
Therefore, the coordinates of D are;
[tex]D(10,-2)[/tex]
Attached below is the graph containing point D;
