Midpoint of a Segment
Algebra, Coordinate Geometry
Intro: Enter two points; get the midpoint coordinates in fraction or decimal form.
Worked example
- Midpoint of $(−3,4)$ and $(5,−2)$.
- Given: $A(x_1,y_1)=(-3,4)$, $B(x_2,y_2)=(5,-2)$.
- Midpoint formula: $$x_m = \frac{x_1+x_2}{2},\quad y_m = \frac{y_1+y_2}{2}.$$
- Compute $x_m$: $$x_m = \frac{-3+5}{2} = \frac{2}{2} = 1.$$
- Compute $y_m$: $$y_m = \frac{4+(-2)}{2} = \frac{2}{2} = 1.$$
- Therefore: $$\boxed{M(1,1)}.$$
- Optional check (vector average): $$\tfrac{1}{2}(A+B)=\tfrac{1}{2}((-3,4)+(5,-2))=\tfrac{1}{2}(2,2)=(1,1).$$ ✔️
FAQs
Return decimals?
We keep exact fractions by default, but you can choose decimal output.
3D midpoint?
Use $\big(\tfrac{x_1+x_2}{2},\tfrac{y_1+y_2}{2},\tfrac{z_1+z_2}{2}\big)$ for points in 3D.
Why choose Mathix?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
Midpoint formula
- x_m = (x1 + x2)/2
- y_m = (y1 + y2)/2
- M(x_m, y_m)