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Find the Midpoint of Line Segment AB: A(2,3) and B(7,3)
Published on August 6, 2024
Geometry
Find the midpoint (M) of line segment AB, given A(2,3) and B(7,3). The midpoint is calculated using the midpoint formula, resulting in M(4.5, 3).
Question
What are the coordinates of M, found halfway between A and B?
Answer
Let’s break this problem down step-by-step.
1. Understand the Problem
We need to find the midpoint (M) of a line segment AB. We are given the coordinates of A (2,3) and B (7,3).
2. Midpoint Formula
The midpoint of a line segment is found by averaging the x-coordinates and the y-coordinates of the endpoints. The formula is:
Midpoint (M) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
3. Apply the Formula
- Let A (2, 3) be (x₁, y₁)
- Let B (7, 3) be (x₂, y₂)
Substitute the values into the midpoint formula:
M = ((2 + 7)/2 , (3 + 3)/2)
4. Calculate the Coordinates
M = (9/2 , 6/2)
M = (4.5, 3)
Answer: The coordinates of M are (4.5, 3).