Given Coordinates and Understanding the Shape

Oct 13, 2025 by miodeya.com 31 views

Understanding the Basics of a Kite

A kite is a type of quadrilateral with two pairs of adjacent sides that are equal in length. This unique property makes the kite a fascinating shape in geometry. In this article, we will explore how to calculate the perimeter of a kite using the given coordinates of its vertices.

Given Coordinates and Understanding the Shape

The vertices of the kite are given as ${$ (2,4), (5,4), (5,1),$}$ and ${$ (0,-1)$}$. To calculate the perimeter, we need to find the lengths of all four sides of the kite. We can use the distance formula to find the length of each side.

Calculating the Length of Each Side

The distance formula is given by:

${d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

We can use this formula to find the length of each side of the kite.

Side 1: From (2,4) to (5,4)

Using the distance formula, we get:

${d_1 = \sqrt{(5 - 2)^2 + (4 - 4)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3}$

Side 2: From (5,4) to (5,1)

Using the distance formula, we get:

${d_2 = \sqrt{(5 - 5)^2 + (1 - 4)^2} = \sqrt{0^2 + (-3)^2} = \sqrt{9} = 3}$

Side 3: From (5,1) to (0,-1)

Using the distance formula, we get:

${d_3 = \sqrt{(0 - 5)^2 + (-1 - 1)^2} = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.4}$

Side 4: From (0,-1) to (2,4)

Using the distance formula, we get:

${d_4 = \sqrt{(2 - 0)^2 + (4 - (-1))^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.4}$

Calculating the Perimeter

Now that we have the lengths of all four sides, we can calculate the perimeter of the kite by adding up the lengths of all four sides.

Perimeter = d1 + d2 + d3 + d4 Perimeter = 3 + 3 + 5.4 + 5.4 Perimeter = 16.8

Conclusion

In this article, we calculated the perimeter of a kite using the given coordinates of its vertices. We used the distance formula to find the length of each side of the kite and then added up the lengths to find the perimeter. The approximate perimeter of the kite is 16.8 units, rounded to the nearest tenth.

Answer

The correct answer is C. 16.8 units.

Understanding the Basics of a Kite

Q&A: Calculating the Perimeter of a Kite

Q: What is the formula to calculate the perimeter of a kite?

A: The formula to calculate the perimeter of a kite is to add up the lengths of all four sides. You can use the distance formula to find the length of each side.

Q: What is the distance formula?

A: The distance formula is given by:

${d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

This formula calculates the distance between two points in a coordinate plane.

Q: How do I use the distance formula to find the length of each side of the kite?

A: To use the distance formula, you need to plug in the coordinates of the two points that make up each side of the kite. For example, to find the length of the side from (2,4) to (5,4), you would plug in x1 = 2, y1 = 4, x2 = 5, and y2 = 4 into the distance formula.

Q: What if the coordinates of the vertices are not given? How do I find the perimeter of the kite?

A: If the coordinates of the vertices are not given, you can use other methods to find the perimeter of the kite. For example, you can use the Pythagorean theorem to find the length of each side, or you can use trigonometry to find the length of each side.

Q: Can I use the distance formula to find the length of a diagonal of the kite?

A: Yes, you can use the distance formula to find the length of a diagonal of the kite. To do this, you need to plug in the coordinates of the two points that make up the diagonal into the distance formula.

Q: What is the relationship between the perimeter of a kite and its diagonals?

A: The perimeter of a kite is equal to the sum of the lengths of its diagonals. This is because the diagonals of a kite intersect at their midpoints, and the sum of the lengths of the diagonals is equal to the perimeter of the kite.

Conclusion

In this article, we answered some common questions about calculating the perimeter of a kite. We discussed the formula to calculate the perimeter of a kite, the distance formula, and how to use the distance formula to find the length of each side of the kite. We also discussed how to find the perimeter of a kite if the coordinates of the vertices are not given, and the relationship between the perimeter of a kite and its diagonals.

Additional Resources

Distance Formula: The distance formula is a mathematical formula that calculates the distance between two points in a coordinate plane.
Pythagorean Theorem: The Pythagorean theorem is a mathematical formula that calculates the length of the hypotenuse of a right triangle.
Trigonometry: Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Answer

The correct answers to the Q&A are:

Q: What is the formula to calculate the perimeter of a kite? A: The formula to calculate the perimeter of a kite is to add up the lengths of all four sides.
Q: What is the distance formula? A: The distance formula is given by: d = √((x2 - x1)^2 + (y2 - y1)^2)
Q: How do I use the distance formula to find the length of each side of the kite? A: To use the distance formula, you need to plug in the coordinates of the two points that make up each side of the kite.
Q: What if the coordinates of the vertices are not given? How do I find the perimeter of the kite? A: If the coordinates of the vertices are not given, you can use other methods to find the perimeter of the kite, such as the Pythagorean theorem or trigonometry.
Q: Can I use the distance formula to find the length of a diagonal of the kite? A: Yes, you can use the distance formula to find the length of a diagonal of the kite.
Q: What is the relationship between the perimeter of a kite and its diagonals? A: The perimeter of a kite is equal to the sum of the lengths of its diagonals.