- (a) Plot the points P(0, 3), Q(3, 0), and R(6, 3) in the coordinate plane. Where must the point S be located so that PQRS is a square?
- (b) Find the area of PQRS.
(a)
To evaluate: The point S of a square PQRS and plot points in the coordinate plane.
Answer to Problem 15T
The point S is
Explanation of Solution
Given:
The coordinates of points of square PQRS is
Formula used:
The distance formula of two points
Where,
Calculation:
Let the coordinates of points be
Find the distance between the points
Substitute 3 for
The distance between two points
Substitute
Since all sides of square are equal in length,
Substitute
From the above expression the equation is,
Substitute
The equation from above expression is,
Subtract equation (2) from equation (1) to get the values of x,
Substitute 3 for x in equation (2) to get value of y.
These values of x- and y-coordinates gives the point S.
Since the point
Thus, the coordinates of point S is
Now the point
In point
The coordinate plane of points of square is shown below in Figure (1).
Figure (1)
From Figure (1), it is observed that the coordinates of the square PQRS are
(b)
To find: The area of square PQRS.
Answer to Problem 15T
The area of square PQRS is 18.
Explanation of Solution
Given:
The coordinates of points of square PQRS is
Calculation:
The formula of area of square is,
From part (a) the side of square PQRS is
Substitute
Thus, the area of square PQRS is 18.
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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