Question

The coordinates of three of the vertices of a rectangle PQRS are P(-2, 2), Q(4, 2), and R(4, -3). A. Find the coordinates of point S, the fourth vertex of rectangle PQRS. B. What is the perimeter of the rectangle PQRS?

Answer 1

The coordinates are (x,y) (-2,-3)

Explanation:

We need to take note of the following properties.

1. A rectangle has 4 sides.

2. Two opposite sides of a rectangle are equal.

Coordinates of the triangle on the graph: P(-2, 2), Q(4, 2), R(4, -3) and S(x,y)

The length of the triangle:

We can get this from the x -coordinates of P and Q

Length = |-2 - 4| = 6 (We are only taking positive values for dimensions. You cannot have a negative length)

Recall that the length of the two sides is equal. Therefore, we can relate the length of the second side to its coordinates using the coordinates of R and S

x = 4-6; x = - 2

The breadth of the triangle

We can get this from the y -coordinates of Q and R

Breadth = |-3 -2| = 5 (We are only taking positive values for dimensions. You cannot have a negative breadth)

Recall that the breadth of the two sides is equal. Therefore, we can relate the breadth of the second side to its coordinates using the coordinates of R and S

2 - y = 5; y = -3

Therefore the coordinates are (x,y) (-2,-3)