Identifying the Coordinates of Polygon ABCDE

Oct 13, 2025 by wbrum.org 0 views

Understanding the Coordinate Grid

The given coordinate grid represents a polygon ABCDE, with specific points marked on it. To calculate the perimeter of this polygon, we need to understand the concept of distance between two points on a coordinate grid. The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Identifying the Coordinates of Polygon ABCDE

From the given coordinate grid, we can identify the coordinates of each point of the polygon ABCDE:

A(2, 5)
B(4, 4)
C(5, 3)
D(4, 2)
E(2, 1)

Calculating the Distance Between Each Pair of Points

To calculate the perimeter of the polygon, we need to calculate the distance between each pair of consecutive points. Let's start with the distance between points A and B:

Distance AB = √((4 - 2)^2 + (4 - 5)^2) Distance AB = √(2^2 + (-1)^2) Distance AB = √(4 + 1) Distance AB = √5 ≈ 2.24

Calculating the Distance Between Points B and C

Next, we calculate the distance between points B and C:

Distance BC = √((5 - 4)^2 + (3 - 4)^2) Distance BC = √(1^2 + (-1)^2) Distance BC = √(1 + 1) Distance BC = √2 ≈ 1.41

Calculating the Distance Between Points C and D

Now, we calculate the distance between points C and D:

Distance CD = √((4 - 5)^2 + (2 - 3)^2) Distance CD = √((-1)^2 + (-1)^2) Distance CD = √(1 + 1) Distance CD = √2 ≈ 1.41

Calculating the Distance Between Points D and E

Next, we calculate the distance between points D and E:

Distance DE = √((2 - 4)^2 + (1 - 2)^2) Distance DE = √((-2)^2 + (-1)^2) Distance DE = √(4 + 1) Distance DE = √5 ≈ 2.24

Calculating the Distance Between Points E and A

Finally, we calculate the distance between points E and A:

Distance EA = √((2 - 2)^2 + (5 - 1)^2) Distance EA = √(0^2 + 4^2) Distance EA = √(0 + 16) Distance EA = √16 = 4

Calculating the Perimeter of Polygon ABCDE

Now that we have calculated the distance between each pair of consecutive points, we can calculate the perimeter of the polygon ABCDE:

Perimeter = Distance AB + Distance BC + Distance CD + Distance DE + Distance EA Perimeter = 2.24 + 1.41 + 1.41 + 2.24 + 4 Perimeter ≈ 10.90

Conclusion

In conclusion, the perimeter of polygon ABCDE, to the nearest hundredth of a unit, is approximately 10.90 units. This calculation demonstrates the importance of understanding the concept of distance between two points on a coordinate grid and applying it to calculate the perimeter of a polygon.

Key Takeaways

The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2)
To calculate the perimeter of a polygon, we need to calculate the distance between each pair of consecutive points.
The perimeter of polygon ABCDE is approximately 10.90 units, to the nearest hundredth of a unit.

Q: What is the formula for calculating the distance between two points on a coordinate grid?

A: The formula for calculating the distance between two points (x1, y1) and (x2, y2) on a coordinate grid is:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Q: How do I calculate the perimeter of a polygon using the distance formula?

A: To calculate the perimeter of a polygon, you need to calculate the distance between each pair of consecutive points. Let's say you have a polygon with points A, B, C, D, and E. You would calculate the distance between points A and B, B and C, C and D, D and E, and E and A, and then add up all these distances to get the perimeter.

Q: What if I have a polygon with more than 5 points? How do I calculate the perimeter?

A: If you have a polygon with more than 5 points, you would simply continue the process of calculating the distance between each pair of consecutive points and adding them up to get the perimeter. For example, if you have a polygon with points A, B, C, D, E, F, and G, you would calculate the distance between points A and B, B and C, C and D, D and E, E and F, and F and G, and then add up all these distances to get the perimeter.

Q: Can I use the distance formula to calculate the perimeter of a polygon with negative coordinates?

A: Yes, you can use the distance formula to calculate the perimeter of a polygon with negative coordinates. The distance formula works with both positive and negative coordinates, so you can use it to calculate the distance between points with negative coordinates.

Q: How do I round the perimeter to the nearest hundredth of a unit?

A: To round the perimeter to the nearest hundredth of a unit, you would round the final answer to two decimal places. For example, if the perimeter is 10.987, you would round it to 10.99.

Q: What if I have a polygon with coordinates that are not integers? How do I calculate the perimeter?

A: If you have a polygon with coordinates that are not integers, you can still use the distance formula to calculate the perimeter. The distance formula works with both integer and non-integer coordinates, so you can use it to calculate the distance between points with non-integer coordinates.

Q: Can I use the distance formula to calculate the perimeter of a polygon with coordinates that are not in the same coordinate system?

A: No, you cannot use the distance formula to calculate the perimeter of a polygon with coordinates that are not in the same coordinate system. The distance formula assumes that the coordinates are in the same coordinate system, so you would need to convert the coordinates to the same system before using the formula.

Q: How do I check my work when calculating the perimeter of a polygon?

A: To check your work when calculating the perimeter of a polygon, you can use a calculator or a computer program to verify your answers. You can also use a ruler or a measuring tape to measure the distance between each pair of points and add them up to get the perimeter.

Q: What if I make a mistake when calculating the perimeter of a polygon? How do I correct it?

A: If you make a mistake when calculating the perimeter of a polygon, you can correct it by re-checking your work and recalculating the perimeter. You can also use a calculator or a computer program to verify your answers and catch any mistakes.

Conclusion

In conclusion, calculating the perimeter of a polygon using the distance formula can be a bit challenging, but with practice and patience, you can master it. Remember to always check your work and verify your answers to ensure accuracy.