A Square Is Drawn On A Coordinate Grid So That Two Diagonally Opposite Vertices Of The Square Have Coordinates (-4, 7) And (2, 1) Work Out The Perimeter Of This Square. < Previous Watch Video Answer
Introduction
In mathematics, a square is a four-sided shape with all sides of equal length. When a square is drawn on a coordinate grid, its vertices can be represented by their coordinates. In this article, we will explore how to calculate the perimeter of a square when two diagonally opposite vertices have given coordinates.
Understanding the Problem
The problem states that a square is drawn on a coordinate grid with two diagonally opposite vertices having coordinates (-4, 7) and (2, 1). To calculate the perimeter of the square, we need to find the length of each side. Since the square has equal sides, we can use the distance formula to find the length of one side and then multiply it by 4 to get the perimeter.
The Distance Formula
The distance formula is a mathematical formula used to find the distance between two points in a coordinate plane. The formula is:
d = β((x2 - x1)^2 + (y2 - y1)^2)
where d is the distance between the two points, (x1, y1) and (x2, y2) are the coordinates of the two points.
Calculating the Length of One Side
To calculate the length of one side of the square, we can use the distance formula with the coordinates of the two diagonally opposite vertices. Let's call the coordinates of the first vertex (-4, 7) and the coordinates of the second vertex (2, 1).
d = β((2 - (-4))^2 + (1 - 7)^2) d = β((6)^2 + (-6)^2) d = β(36 + 36) d = β72 d = β(36 * 2) d = β36 * β2 d = 6β2
Now that we have the length of one side, we can multiply it by 4 to get the perimeter of the square.
Calculating the Perimeter
The perimeter of a square is the sum of the lengths of all its sides. Since the square has equal sides, we can multiply the length of one side by 4 to get the perimeter.
P = 4 * d P = 4 * 6β2 P = 24β2
Simplifying the Perimeter
To simplify the perimeter, we can rationalize the denominator by multiplying the numerator and denominator by β2.
P = 24β2 P = (24 * β2) / 1 P = (24 * β2 * β2) / (β2 * β2) P = 24 * 2 / 2 P = 48 / 2 P = 24
Conclusion
In this article, we calculated the perimeter of a square drawn on a coordinate grid with two diagonally opposite vertices having coordinates (-4, 7) and (2, 1). We used the distance formula to find the length of one side and then multiplied it by 4 to get the perimeter. The perimeter of the square is 24 units.
Further Reading
If you want to learn more about coordinate geometry and how to calculate distances and perimeters, check out the following resources:
Related Topics
Glossary
- Coordinate Grid: A grid of points with coordinates (x, y) used to represent geometric shapes.
- Distance Formula: A mathematical formula used to find the distance between two points in a coordinate plane.
- Perimeter: The sum of the lengths of all the sides of a shape.
- Square: A four-sided shape with all sides of equal length.
A Square on a Coordinate Grid: Q&A =====================================
Introduction
In our previous article, we calculated the perimeter of a square drawn on a coordinate grid with two diagonally opposite vertices having coordinates (-4, 7) and (2, 1). In this article, we will answer some frequently asked questions related to the topic.
Q: What is the formula for calculating the perimeter of a square?
A: The formula for calculating the perimeter of a square is P = 4 * d, where d is the length of one side of the square.
Q: How do I calculate the length of one side of a square on a coordinate grid?
A: To calculate the length of one side of a square on a coordinate grid, you can use the distance formula: d = β((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Q: What is the distance formula?
A: The distance formula is a mathematical formula used to find the distance between two points in a coordinate plane. The formula is d = β((x2 - x1)^2 + (y2 - y1)^2), where d is the distance between the two points.
Q: How do I simplify the perimeter of a square?
A: To simplify the perimeter of a square, you can rationalize the denominator by multiplying the numerator and denominator by β2.
Q: What is the perimeter of a square with side length 6β2?
A: The perimeter of a square with side length 6β2 is 24 units.
Q: Can I use the distance formula to find the length of a diagonal of a square?
A: Yes, you can use the distance formula to find the length of a diagonal of a square. The formula is d = β((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Q: How do I find the coordinates of the vertices of a square on a coordinate grid?
A: To find the coordinates of the vertices of a square on a coordinate grid, you can use the distance formula to find the length of one side of the square and then use the coordinates of one vertex to find the coordinates of the other vertices.
Q: Can I use a calculator to find the perimeter of a square?
A: Yes, you can use a calculator to find the perimeter of a square. Simply enter the length of one side of the square and multiply it by 4 to get the perimeter.
Conclusion
In this article, we answered some frequently asked questions related to the topic of calculating the perimeter of a square on a coordinate grid. We hope that this article has been helpful in clarifying any doubts you may have had.
Further Reading
If you want to learn more about coordinate geometry and how to calculate distances and perimeters, check out the following resources:
Related Topics
Glossary
- Coordinate Grid: A grid of points with coordinates (x, y) used to represent geometric shapes.
- Distance Formula: A mathematical formula used to find the distance between two points in a coordinate plane.
- Perimeter: The sum of the lengths of all the sides of a shape.
- Square: A four-sided shape with all sides of equal length.