
Concept explainers
To calculate: The coordinates of the point S so that quadrilateral PQRS is a parallelogram.

Answer to Problem 45E
The coordinates of point S so that PQRS forms a parallelogram is
Explanation of Solution
Given information:
The points
Formula used:
A parallelogram is a quadrilateral in which diagonals bisect each other at the same point.
Mid-point formula between two points
Calculation:
Consider the provided vertices
By plotting the given points on the coordinate plane, we get the following figure,
Recall that a parallelogram is a quadrilateral in which diagonals bisect each other at the same point.
So, to find the coordinates of S such that PQRS forms a parallelogram, the mid-point of its diagonals i.e. PR and QS must be equal.
Let the coordinates of the point be
Recall that the mid-point formula between two points
So, midpoint of PR is calculated as,
Now, midpoint of QS is calculated as,
Since, diagonals of a parallelogram bisect each other at same point, so midpoint of PR and QS is same.
So, equate the mid-points of PR and QS as,
Now, equate x-coordinate and y-coordinate from both sides of the equation as,
Thus, the coordinates of point S so that PQRS forms a parallelogram is
Chapter 1 Solutions
Precalculus - A Custom Text for UNLV
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