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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.8, Problem 22E

To determine

**To calculate: **The location of the point S so that quadrilateral PQRS is a square and area of the square along with figure.

Expert Solution

The coordinates of point S so that PQRS forms a square is

**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