Coordinate Geometry Calculator : Free Coordinate Geometry Calculator. Calculate distance, midpoint, slope, and equation of a line between two points on a 2D plane.
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Coordinate Geometry: Theory & Fundamentals
Distance Formula
The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is derived from the Pythagorean theorem: $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. This represents the length of the straight-line segment connecting them.
Slope & Intercepts
The slope $(m)$ defines the steepness of the line, calculated as $\frac{y_2-y_1}{x_2-x_1}$. The line equation $y = mx + b$ allows us to find exactly where the line passes through the plane.
What is the Midpoint Formula?
The midpoint is the average of your coordinates: $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$. It represents the exact center point between P1 and P2.
Why is the slope undefined for vertical lines?
A vertical line has no ‘run’ ($x_2-x_1 = 0$). Since you cannot divide by zero, the slope is undefined, and the equation simplifies to $x = c$.
How do I interpret the line equation?
In $y = mx + b$, ‘m’ is the slope (rise/run) and ‘b’ is the y-intercept, where the line crosses the y-axis.