Find all possible coordinates for S if P, Q, R and S are vertices of a parallelogram?
Given P = (-1, 2), Q = (5, 5), R = (2, -1) are points in the plane.
Solve by using vectors. Also, why would S have other "possible coordinates"? Could there be more than one pair of coordinates for S?
Given P = (-1, 2), Q = (5, 5), R = (2, -1) are points in the plane.
Solve by using vectors. Also, why would S have other "possible coordinates"? Could there be more than one pair of coordinates for S?
1 Answer
I don't have time to write up a full solution tonight, but maybe this will help:
Explanation:
In this problem, we are given 3 points P, Q, and R, and asked to find all possibilities for a 4th point S that will define a parallelogram.
To think about this problem visually, picture the Triforce.
Imagine P, Q, and R as the vertices of the triangle at the center of the Triforce.
There are 3 possibilities for S: the three points at the tips of the Triforce.
Now I leave it up to you to figure out how to determine those points.
Keep in mind that opposite sides of a parallelogram are equal in length.
Hope this helps you figure it out!
