To evaluate: The point S of a square PQRS and plot points in the coordinate plane.
The point S is .
The coordinates of points of square PQRS is , and .
The distance formula of two points and is,
Where, is the distance between two points and , , and are coordinates of two points.
Let the coordinates of points be .
Find the distance between the points and .
Substitute 3 for , 0 for , 0 for and 3 for in formula (1).
The distance between two points and give another side of square.
Substitute for , 6 for , for and 3 for in formula (1).
Since all sides of square are equal in length, .
Substitute for in .
From the above expression the equation is,
Substitute for to get the distance between point and .
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 exists already in square, so take in point .
Thus, the coordinates of point S is
Now the point is obtained.
In point , x-coordinate is zero, so it is lies in y-axis similarly point lies on x-axis and points , both coordinates are positive so it is lies in I Quadrant.
The coordinate plane of points of square is shown below in Figure (1).
From Figure (1), it is observed that the coordinates of the square PQRS are , and and .
To find: The area of square PQRS.
The area of square PQRS is 18.
The coordinates of points of square PQRS is , , .
The formula of area of square is,
From part (a) the side of square PQRS is .
Substitute for side in the formula of area of square.
Thus, the area of square PQRS is 18.
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