What Is The Midpoint Of A Line Segment With The Endpoints \[$(8, -3)\$\] And \[$(-5, -9)\$\]?A. \[$(1.5, -6)\$\] B. \[$(2.5, -7)\$\] C. \[$(-7, 2.5)\$\] D. \[$(-6, 1.5)\$\]
Introduction to Midpoint Formula
The midpoint of a line segment is the point that divides the line segment into two equal parts. It is the average of the x-coordinates and the average of the y-coordinates of the endpoints of the line segment. The midpoint formula is used to find the midpoint of a line segment given the coordinates of its endpoints.
Midpoint Formula
The midpoint formula is given by:
(x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Example Problem
Find the midpoint of a line segment with the endpoints (8, -3) and (-5, -9).
Step 1: Identify the Coordinates of the Endpoints
The coordinates of the endpoints are (8, -3) and (-5, -9).
Step 2: Apply the Midpoint Formula
To find the midpoint, we need to apply the midpoint formula:
(x1 + x2)/2, (y1 + y2)/2)
Substituting the values of the coordinates, we get:
(8 + (-5))/2, (-3 + (-9))/2)
Step 3: Simplify the Expression
Simplifying the expression, we get:
(3)/2, (-12)/2)
Step 4: Evaluate the Expression
Evaluating the expression, we get:
(3/2, -6)
Step 5: Write the Midpoint in the Correct Format
The midpoint is written in the format (x, y), where x is the x-coordinate and y is the y-coordinate.
Step 6: Compare the Answer with the Options
Comparing the answer with the options, we get:
(3/2, -6) = (1.5, -6)
Conclusion
The midpoint of the line segment with the endpoints (8, -3) and (-5, -9) is (1.5, -6).
Final Answer
The final answer is:
(1.5, -6)
Discussion
The midpoint formula is a useful tool for finding the midpoint of a line segment given the coordinates of its endpoints. It is a simple and efficient way to find the midpoint, and it is widely used in mathematics and other fields.
Importance of Midpoint Formula
The midpoint formula is important because it allows us to find the midpoint of a line segment given the coordinates of its endpoints. This is useful in a variety of situations, such as:
- Finding the midpoint of a line segment in a coordinate plane
- Finding the midpoint of a line segment in a three-dimensional space
- Finding the midpoint of a line segment in a real-world application, such as finding the midpoint of a road or a river
Real-World Applications
The midpoint formula has a variety of real-world applications, such as:
- Finding the midpoint of a road or a river
- Finding the midpoint of a building or a structure
- Finding the midpoint of a line segment in a three-dimensional space
Conclusion
In conclusion, the midpoint formula is a useful tool for finding the midpoint of a line segment given the coordinates of its endpoints. It is a simple and efficient way to find the midpoint, and it is widely used in mathematics and other fields.
Final Thoughts
The midpoint formula is an important concept in mathematics, and it has a variety of real-world applications. It is a useful tool for finding the midpoint of a line segment given the coordinates of its endpoints, and it is widely used in mathematics and other fields.
References
Related Topics
Further Reading
Introduction
The midpoint formula is a fundamental concept in mathematics that allows us to find the midpoint of a line segment given the coordinates of its endpoints. In this article, we will answer some frequently asked questions about the midpoint formula.
Q1: What is the midpoint formula?
A1: The midpoint formula is a mathematical formula that allows us to find the midpoint of a line segment given the coordinates of its endpoints. The formula is given by:
(x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Q2: How do I apply the midpoint formula?
A2: To apply the midpoint formula, you need to follow these steps:
- Identify the coordinates of the endpoints of the line segment.
- Substitute the values of the coordinates into the midpoint formula.
- Simplify the expression.
- Evaluate the expression.
Q3: What is the midpoint of a line segment with endpoints (2, 3) and (4, 5)?
A3: To find the midpoint, we need to apply the midpoint formula:
(2 + 4)/2, (3 + 5)/2)
Simplifying the expression, we get:
(6)/2, (8)/2)
Evaluating the expression, we get:
(3, 4)
Q4: What is the midpoint of a line segment with endpoints (-2, 1) and (3, -4)?
A4: To find the midpoint, we need to apply the midpoint formula:
(-2 + 3)/2, (1 + (-4))/2)
Simplifying the expression, we get:
(1)/2, (-3)/2)
Evaluating the expression, we get:
(0.5, -1.5)
Q5: Can I use the midpoint formula to find the midpoint of a line segment in a three-dimensional space?
A5: Yes, you can use the midpoint formula to find the midpoint of a line segment in a three-dimensional space. The formula is given by:
(x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)
where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the endpoints of the line segment.
Q6: What is the midpoint of a line segment with endpoints (1, 2, 3) and (4, 5, 6)?
A6: To find the midpoint, we need to apply the midpoint formula:
(1 + 4)/2, (2 + 5)/2, (3 + 6)/2)
Simplifying the expression, we get:
(5)/2, (7)/2, (9)/2)
Evaluating the expression, we get:
(2.5, 3.5, 4.5)
Q7: Can I use the midpoint formula to find the midpoint of a line segment in a real-world application?
A7: Yes, you can use the midpoint formula to find the midpoint of a line segment in a real-world application. For example, you can use the midpoint formula to find the midpoint of a road or a river.
Q8: What is the midpoint of a line segment with endpoints (10, 20) and (30, 40)?
A8: To find the midpoint, we need to apply the midpoint formula:
(10 + 30)/2, (20 + 40)/2)
Simplifying the expression, we get:
(40)/2, (60)/2)
Evaluating the expression, we get:
(20, 30)
Conclusion
In conclusion, the midpoint formula is a useful tool for finding the midpoint of a line segment given the coordinates of its endpoints. It is a simple and efficient way to find the midpoint, and it is widely used in mathematics and other fields.
Final Thoughts
The midpoint formula is an important concept in mathematics, and it has a variety of real-world applications. It is a useful tool for finding the midpoint of a line segment given the coordinates of its endpoints, and it is widely used in mathematics and other fields.