To calculate: The location of the point S so that quadrilateral PQRS is a square and area of the square along with figure.
Answer to Problem 22E
The coordinates of point S so that PQRS forms a square is
Explanation of Solution
Given information:
The points
Formula used:
A square is a special kind of quadrilateral having equal lengths of its sides and diagonals.
Distance formula between two points
Area of a square with its side length x is the square of its side, which is mathematically written as,
Calculation:
Consider the provided vertices
By plotting the given points on the coordinate plane, we get the following figure,
Recall that a square is a special kind of quadrilateral having equal lengths of its sides and diagonals.
So, to find the coordinates of S such that PQRS forms a square, the lengths of its diagonals i.e. PR and QS must be equal.
For the coordinates to form a square, S must lie on y-axis, so, assume the coordinates of S as
Now, apply distance formula between two points
Simplify it further as,
Therefore, the fourth vertex of the square PQRS is at point
Now, the length of side of square is calculated as,
Recall that area of a square with its side length x is the square of its side, which is mathematically written as,
So, area of square PQRS is calculated as,
Thus, the coordinates of point S so that PQRS forms a square is
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning