The Coordinates of the Vertices of the Rectangle

Oct 13, 2025 by magicalceylontours.com 56 views

Introduction

In geometry, a rectangle is a quadrilateral with four right angles and opposite sides of equal length. The coordinates of the vertices of a rectangle can be used to find various properties of the rectangle, such as the distance between two points. In this article, we will use the coordinates of the vertices of a rectangle to find the distance between two points.

The Coordinates of the Vertices of the Rectangle

The coordinates of the vertices of the rectangle are given as:

A(5, 3)
B(5, -9)
C(-1, -9)
D(-1, 3)

What is the Distance Between Two Points?

The distance between two points in a coordinate plane is the length of the line segment connecting the two points. To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between the two points, and (x1, y1) and (x2, y2) are the coordinates of the two points.

Finding the Distance Between Point B and Point C

To find the distance between point B and point C, we can use the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) = (5, -9) and (x2, y2) = (-1, -9).

d = √((-1 - 5)² + (-9 - (-9))²) d = √((-6)² + 0²) d = √(36 + 0) d = √36 d = 6

Finding the Distance Between Point B and Point D

To find the distance between point B and point D, we can use the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) = (5, -9) and (x2, y2) = (-1, 3).

d = √((-1 - 5)² + (3 - (-9))²) d = √((-6)² + (12)²) d = √(36 + 144) d = √180 d ≈ 13.416

Finding the Distance Between Point B and Point A

To find the distance between point B and point A, we can use the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) = (5, -9) and (x2, y2) = (5, 3).

d = √((5 - 5)² + (3 - (-9))²) d = √(0² + (12)²) d = √(0 + 144) d = √144 d = 12

Conclusion

In this article, we used the coordinates of the vertices of a rectangle to find the distance between two points. We found the distance between point B and point C to be 6 units, the distance between point B and point D to be approximately 13.416 units, and the distance between point B and point A to be 12 units.

Discussion

Which measurement is closest to the distance between point B and point C?

5 units
6 units
7 units
8 units

Q: What is the formula for finding the distance between two points in a coordinate plane?

A: The formula for finding the distance between two points in a coordinate plane is:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between the two points, and (x1, y1) and (x2, y2) are the coordinates of the two points.

Q: How do I use the distance formula to find the distance between two points?

A: To use the distance formula, you need to substitute the coordinates of the two points into the formula. For example, if you want to find the distance between points A(5, 3) and B(5, -9), you would substitute x1 = 5, y1 = 3, x2 = 5, and y2 = -9 into the formula.

Q: What is the distance between point B and point C in the given rectangle?

A: The distance between point B and point C is 6 units.

Q: What is the distance between point B and point D in the given rectangle?

A: The distance between point B and point D is approximately 13.416 units.

Q: What is the distance between point B and point A in the given rectangle?

A: The distance between point B and point A is 12 units.

Q: How do I find the length of the sides of the rectangle?

A: To find the length of the sides of the rectangle, you can use the distance formula to find the distance between the vertices of the rectangle. For example, you can find the distance between points A and B, points B and C, points C and D, and points D and A.

Q: What is the perimeter of the rectangle?

A: The perimeter of the rectangle is the sum of the lengths of all its sides. To find the perimeter, you need to find the length of each side and add them together.

Q: What is the area of the rectangle?

A: The area of the rectangle is the product of its length and width. To find the area, you need to find the length and width of the rectangle and multiply them together.

Q: How do I find the length and width of the rectangle?

A: To find the length and width of the rectangle, you can use the distance formula to find the distance between the vertices of the rectangle. For example, you can find the distance between points A and B to get the length, and the distance between points B and C to get the width.

Q: What is the formula for finding the area of a rectangle?

A: The formula for finding the area of a rectangle is:

Area = length × width

Q: What is the formula for finding the perimeter of a rectangle?

A: The formula for finding the perimeter of a rectangle is:

Perimeter = 2 × (length + width)

Conclusion

In this article, we answered some common questions about finding the distance between two points in a coordinate plane, and finding the length and width of a rectangle. We also discussed how to find the perimeter and area of a rectangle.