Find the Midpoint of Line Segment AB: A(2,3) and B(7,3)
Published on August 6, 2024
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).