Given the coordinates of points $A(-2, 1)$, $B(1, 0)$, and $C(2, 4)$, find the coordinates of point $E$ such that quadrilateral $ABEC$ is a parallelogram.
2025/5/11
1. Problem Description
Given the coordinates of points , , and , find the coordinates of point such that quadrilateral is a parallelogram.
2. Solution Steps
In a parallelogram, opposite sides are parallel and equal in length. In parallelogram , we have and . Also, and .
Let . We can use to find the coordinates of .
Since , we have:
and
Therefore, .
We can also use .
Since , we have:
and
Therefore, .
3. Final Answer
The coordinates of point are .