Finding the Coordinates of the Other Vertices

Oct 13, 2025 by windailys.com 99 views

Introduction

In this article, we will explore the problem of drawing a square with one vertex at the point (-3, 5) and a perimeter of 20 units. We will use the concept of geometry and coordinate geometry to find the coordinates of each other vertex.

Understanding the Problem

To draw a square with a perimeter of 20 units, we need to find the length of each side. Since the perimeter of a square is equal to 4 times the length of one side, we can calculate the length of each side as follows:

Perimeter = 4 × side length 20 = 4 × side length side length = 20/4 side length = 5 units

Finding the Coordinates of the Other Vertices

Since the square has a side length of 5 units, we can find the coordinates of the other vertices by moving 5 units horizontally and vertically from the given vertex (-3, 5).

Moving Horizontally

To move horizontally, we need to add or subtract the side length from the x-coordinate of the given vertex. Since we are moving to the right, we will add the side length to the x-coordinate.

x-coordinate of the given vertex = -3 side length = 5 x-coordinate of the new vertex = -3 + 5 x-coordinate of the new vertex = 2

Moving Vertically

To move vertically, we need to add or subtract the side length from the y-coordinate of the given vertex. Since we are moving upwards, we will add the side length to the y-coordinate.

y-coordinate of the given vertex = 5 side length = 5 y-coordinate of the new vertex = 5 + 5 y-coordinate of the new vertex = 10

Finding the Coordinates of the Other Vertices

Now that we have found the coordinates of one new vertex (2, 10), we can find the coordinates of the other vertices by moving 5 units horizontally and vertically from this vertex.

Vertex 1

x-coordinate of the given vertex = -3 side length = 5 x-coordinate of the new vertex = -3 + 5 x-coordinate of the new vertex = 2 y-coordinate of the new vertex = 10 Vertex 1: (2, 10)

Vertex 2

x-coordinate of the given vertex = 2 side length = 5 x-coordinate of the new vertex = 2 + 5 x-coordinate of the new vertex = 7 y-coordinate of the given vertex = 10 y-coordinate of the new vertex = 10 Vertex 2: (7, 10)

Vertex 3

x-coordinate of the given vertex = 7 side length = 5 x-coordinate of the new vertex = 7 + 5 x-coordinate of the new vertex = 12 y-coordinate of the given vertex = 10 y-coordinate of the new vertex = 10 Vertex 3: (12, 10)

Vertex 4

x-coordinate of the given vertex = 12 side length = 5 x-coordinate of the new vertex = 12 - 5 x-coordinate of the new vertex = 7 y-coordinate of the given vertex = 10 y-coordinate of the new vertex = 10 Vertex 4: (7, 10)

Conclusion

In this article, we have found the coordinates of each other vertex of a square with one vertex at the point (-3, 5) and a perimeter of 20 units. We have used the concept of geometry and coordinate geometry to find the coordinates of each other vertex.

Step-by-Step Solution

Here is a step-by-step solution to the problem:

Find the length of each side of the square by dividing the perimeter by 4.
Move 5 units horizontally and vertically from the given vertex to find the coordinates of one new vertex.
Move 5 units horizontally and vertically from the new vertex to find the coordinates of the other vertices.
Repeat step 3 until all vertices have been found.

Example

Here is an example of how to find the coordinates of each other vertex of a square with one vertex at the point (-3, 5) and a perimeter of 20 units.

Suppose we want to find the coordinates of the other vertices of a square with one vertex at the point (-3, 5) and a perimeter of 20 units.

Find the length of each side of the square by dividing the perimeter by 4. Perimeter = 20 side length = 20/4 side length = 5 units
Move 5 units horizontally and vertically from the given vertex to find the coordinates of one new vertex. x-coordinate of the given vertex = -3 side length = 5 x-coordinate of the new vertex = -3 + 5 x-coordinate of the new vertex = 2 y-coordinate of the given vertex = 5 side length = 5 y-coordinate of the new vertex = 5 + 5 y-coordinate of the new vertex = 10 Vertex 1: (2, 10)
Move 5 units horizontally and vertically from the new vertex to find the coordinates of the other vertices. x-coordinate of the new vertex = 2 side length = 5 x-coordinate of the new vertex = 2 + 5 x-coordinate of the new vertex = 7 y-coordinate of the new vertex = 10 y-coordinate of the new vertex = 10 Vertex 2: (7, 10)
Repeat step 3 until all vertices have been found. x-coordinate of the new vertex = 7 side length = 5 x-coordinate of the new vertex = 7 + 5 x-coordinate of the new vertex = 12 y-coordinate of the new vertex = 10 y-coordinate of the new vertex = 10 Vertex 3: (12, 10) x-coordinate of the new vertex = 12 side length = 5 x-coordinate of the new vertex = 12 - 5 x-coordinate of the new vertex = 7 y-coordinate of the new vertex = 10 y-coordinate of the new vertex = 10 Vertex 4: (7, 10)

Code

Here is a Python code snippet that can be used to find the coordinates of each other vertex of a square with one vertex at the point (-3, 5) and a perimeter of 20 units.

def find_vertices(x, y, perimeter):
    # Find the length of each side of the square
    side_length = perimeter / 4
# Move 5 units horizontally and vertically from the given vertex to find the coordinates of one new vertex
new_x = x + side_length
new_y = y + side_length

# Move 5 units horizontally and vertically from the new vertex to find the coordinates of the other vertices
vertices = [(new_x, new_y)]
for _ in range(3):
    new_x += side_length
    new_y = y
    vertices.append((new_x, new_y))
    new_x += side_length
    new_y += side_length
    vertices.append((new_x, new_y))

return vertices

x = -3
y = 5
perimeter = 20
vertices = find_vertices(x, y, perimeter)
print(vertices)

Conclusion

Introduction

In our previous article, we explored the problem of drawing a square with one vertex at the point (-3, 5) and a perimeter of 20 units. We used the concept of geometry and coordinate geometry to find the coordinates of each other vertex. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the length of each side of the square?

A: The length of each side of the square is 5 units.

Q: How do I find the coordinates of the other vertices of the square?

A: To find the coordinates of the other vertices of the square, you need to move 5 units horizontally and vertically from the given vertex. You can use the formula:

x-coordinate of the new vertex = x-coordinate of the given vertex + side length y-coordinate of the new vertex = y-coordinate of the given vertex + side length

Q: What is the formula for finding the coordinates of the other vertices of the square?

A: The formula for finding the coordinates of the other vertices of the square is:

x-coordinate of the new vertex = x-coordinate of the given vertex + side length y-coordinate of the new vertex = y-coordinate of the given vertex + side length

Q: How do I find the coordinates of the vertices of the square if the given vertex is at (x, y)?

A: To find the coordinates of the vertices of the square if the given vertex is at (x, y), you need to use the formula:

x-coordinate of the new vertex = x-coordinate of the given vertex + side length y-coordinate of the new vertex = y-coordinate of the given vertex + side length

Q: What is the perimeter of the square?

A: The perimeter of the square is 20 units.

Q: How do I find the perimeter of the square?

A: To find the perimeter of the square, you need to multiply the length of each side by 4.

Q: What is the area of the square?

A: The area of the square is not required to solve this problem.

Q: How do I find the area of the square?

A: To find the area of the square, you need to multiply the length of each side by itself.

Q: What is the formula for finding the area of the square?

A: The formula for finding the area of the square is:

Area = side length × side length

Q: How do I find the coordinates of the vertices of the square if the given vertex is at (-3, 5)?

A: To find the coordinates of the vertices of the square if the given vertex is at (-3, 5), you need to use the formula:

x-coordinate of the new vertex = x-coordinate of the given vertex + side length y-coordinate of the new vertex = y-coordinate of the given vertex + side length

Q: What are the coordinates of the vertices of the square if the given vertex is at (-3, 5)?

A: The coordinates of the vertices of the square if the given vertex is at (-3, 5) are:

Vertex 1: (2, 10) Vertex 2: (7, 10) Vertex 3: (12, 10) Vertex 4: (7, 5)

Conclusion

In this article, we have answered some frequently asked questions related to the problem of drawing a square with one vertex at the point (-3, 5) and a perimeter of 20 units. We have used the concept of geometry and coordinate geometry to find the coordinates of each other vertex.

Step-by-Step Solution

Here is a step-by-step solution to the problem:

Find the length of each side of the square by dividing the perimeter by 4.
Move 5 units horizontally and vertically from the given vertex to find the coordinates of one new vertex.
Move 5 units horizontally and vertically from the new vertex to find the coordinates of the other vertices.
Repeat step 3 until all vertices have been found.

Example

Here is an example of how to find the coordinates of each other vertex of a square with one vertex at the point (-3, 5) and a perimeter of 20 units.

Suppose we want to find the coordinates of the other vertices of a square with one vertex at the point (-3, 5) and a perimeter of 20 units.

Find the length of each side of the square by dividing the perimeter by 4. Perimeter = 20 side length = 20/4 side length = 5 units
Move 5 units horizontally and vertically from the given vertex to find the coordinates of one new vertex. x-coordinate of the given vertex = -3 side length = 5 x-coordinate of the new vertex = -3 + 5 x-coordinate of the new vertex = 2 y-coordinate of the given vertex = 5 side length = 5 y-coordinate of the new vertex = 5 + 5 y-coordinate of the new vertex = 10 Vertex 1: (2, 10)
Move 5 units horizontally and vertically from the new vertex to find the coordinates of the other vertices. x-coordinate of the new vertex = 2 side length = 5 x-coordinate of the new vertex = 2 + 5 x-coordinate of the new vertex = 7 y-coordinate of the new vertex = 10 y-coordinate of the new vertex = 10 Vertex 2: (7, 10)
Repeat step 3 until all vertices have been found. x-coordinate of the new vertex = 7 side length = 5 x-coordinate of the new vertex = 7 + 5 x-coordinate of the new vertex = 12 y-coordinate of the new vertex = 10 y-coordinate of the new vertex = 10 Vertex 3: (12, 10) x-coordinate of the new vertex = 12 side length = 5 x-coordinate of the new vertex = 12 - 5 x-coordinate of the new vertex = 7 y-coordinate of the new vertex = 10 y-coordinate of the new vertex = 10 Vertex 4: (7, 10)

Code

Here is a Python code snippet that can be used to find the coordinates of each other vertex of a square with one vertex at the point (-3, 5) and a perimeter of 20 units.

def find_vertices(x, y, perimeter):
    # Find the length of each side of the square
    side_length = perimeter / 4
# Move 5 units horizontally and vertically from the given vertex to find the coordinates of one new vertex
new_x = x + side_length
new_y = y + side_length

# Move 5 units horizontally and vertically from the new vertex to find the coordinates of the other vertices
vertices = [(new_x, new_y)]
for _ in range(3):
    new_x += side_length
    new_y = y
    vertices.append((new_x, new_y))
    new_x += side_length
    new_y += side_length
    vertices.append((new_x, new_y))

return vertices

x = -3
y = 5
perimeter = 20
vertices = find_vertices(x, y, perimeter)
print(vertices)