Algebra

##### Related Lessons

- Adding and Subtracting Scientific Notation
- Adding Fractions
- Algebra Calculators
- Arithmetic Sequence
- Average Rate of Change
- Change of Base Formula
- Cm to M
- Commutative Property of Addition
- Completing the Square
- Cross Product Calculator
- Determinant Calculator
- Determinant of a Matrix
- Difference of Squares
- Discriminant
- Divisibility Rule for 7
- Dot Product Calculator
- Eigenvalue Calculator
- Eigenvector Calculator
- Equation of a Circle
- Even Numbers
- Exponent Rules
- Factorial Calculator
- Fractional Exponents
- How to Find the Median
- Interval Notation
- Matrix Addition
- Matrix Subtraction
- Midpoint Formula
- Multiplying Negative Numbers
- Negative Exponents
- Odd Numbers
- One to One Function
- Partial Fraction Decomposition Calculator
- Point Slope Form
- Properties of Multiplication
- Rationalize the Denominator
- Rectangular to Polar Calculator
- Reflexive Property
- Round to the Nearest Tenth
- RREF Calculator
- Slope Intercept Form
- Standard Form
- Summation Calculator
- Vertex Form

Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# Midpoint Formula

## Definition of the Midpoint Formula

The midpoint formula gives us the center point on a line between two points. It is given as:**(x, y) = ( ^{(x1 + x2)}⁄_{2} , ^{(y1 + y2)}⁄_{2})**

The x and y coordinates used in the formula come from the two end points of the line being examined. This formula gives us the exact midpoint of a straight line.

### Where the Formula Comes From

**The midpoint formula takes the average of the line’s endpoints.** The first term in the formula sums x_{1} and x_{2}, then divides that sum by two. The second term in the formula sums y_{1} and y_{2}, then divides that sum by two.

We know that a straight line is simply a connection between two points in the coordinate system. Its midpoint is also considered a point in the coordinate system. This is why the midpoint formula is in the format of coordinates for a point. Take a look at the image above for a visual of how the midpoint formula is derived.

### Example Problems

**Problem 1:**

What is the midpoint of the line generated by the points (5 , 4) and (6 , 7)?

Solution:

(5 + 6)/2 = 5.5, and (4 + 7)/2 = 5.5**The midpoint of the line is (5.5, 5.5)**.

**Problem 2:**

A line has an endpoint at (0, 2) and its midpoint is at (8, 4). What is the other endpoint?

Solution:

Let’s work backwards through the midpoint formula. ^{0 + x2}/_{2} = 8, so x_{2} = 16. Then, ^{2 + y2}/_{2} = 4, so y_{2} = 6.**The other endpoint is (16, 6)**.

**Problem 3:**

A line has two endpoints given as (-3, -3) and (12, 5). What is the midpoint of the line?

Solution:

(-3 + 12)/2 = 4.5, and (-3 + 5)/2 = 1**The midpoint of the line is (4.5, 1)**.

Result :

Worksheet 1

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Cheat sheet

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