The Midpoint Formula
Apply the midpoint formula in Grade 9 algebra. Calculate M=((x₁+x₂)/2,(y₁+y₂)/2) between two coordinate points to find segment bisectors and solve coordinate geometry problems.
Key Concepts
Property The midpoint $M$ of the line segment with endpoints $(x 1, y 1)$ and $(x 2, y 2)$ is $$M = \left(\frac{x 1 + x 2}{2}, \frac{y 1 + y 2}{2}\right)$$.
Explanation Finding the exact middle of a line is as easy as finding an average, just like the lesson hints! This formula averages the x values to get the new x coordinate and averages the y values for the new y coordinate, landing you perfectly in the center.
Examples Find the midpoint of a segment with endpoints $(3, 5)$ and $(7, 2)$: $M = \left(\frac{3 + 7}{2}, \frac{5 + ( 2)}{2}\right) = \left(5, \frac{3}{2}\right)$. Find the midpoint between $( 2, 3)$ and $(4, 7)$: $M = \left(\frac{ 2 + 4}{2}, \frac{3 + 7}{2}\right) = \left(\frac{2}{2}, \frac{10}{2}\right) = (1, 5)$.
Common Questions
What is the midpoint formula and how do you use it?
Midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂) is M = ((x₁+x₂)/2, (y₁+y₂)/2). Average the x-coordinates and y-coordinates separately.
How do you find the midpoint between (2, 4) and (8, -2)?
Average x: (2+8)/2 = 5. Average y: (4+(-2))/2 = 1. The midpoint is (5, 1) — the point exactly halfway between the two endpoints.
How do you find an endpoint if you know the midpoint and one endpoint?
Use the midpoint formula in reverse. If M = (5, 3) and one endpoint is (2, 1): x₂ = 2(5) - 2 = 8, y₂ = 2(3) - 1 = 5. The missing endpoint is (8, 5).