How to Find Missing Coordinates With Slope

By Mark Stansberry
Use the slope of a line to find a missing coordinate.

Being able to find the missing coordinates on a line is often a problem you need to solve to program video games, do well in your algebra class or be proficient in solving coordinate geometry problems. If you want to become an architect, an engineer or a draftsman, you will need to find missing coordinates as part of your job. A common algebra problem requires that you find a missing coordinate (either x or y) given the slope of the line, one pair of known (x, y) coordinates and another (x, y) coordinate pair that has only one known coordinate.

Write down the formula for the slope of the line as M = (Y2 - Y1)/(X2 - X1), where M is the slope of the line, Y2 is the y-coordinate of a point called "A" on the line, X2 is the x-coordinate of point "A," Y1 is the y-coordinate of a point called "B" on the line and X1 is the x-coordinate of point B.

Substitute the value of the slope given and the given coordinate values of point A and point B. Use a slope of "1" and the coordinates of point A as (0, 0) for the point (X2, Y2) and the coordinates of point B as (1, Y1) for the other point (X1, Y1), where Y1 is the unknown coordinate that you must solve for. Check that after you substitute these values into the slope formula that the slope equation reads 1 = (0 - Y1)/(0 - 1).

Solve for the missing coordinate by algebraically manipulating the equation such that the missing coordinate variable is on the left side of the equation and actual coordinate value you must solve for is on the right side of the equation. Use the "Basic Rules of Algebra" link (see Resources) if you are not familiar with solving algebraic equations.

Observe that for this example, the equation, 1 = (0 - Y1)/(0 - 1), simplifies to 1 = -Y1/-1 since subtracting a number from 0 is the negative of the number itself. And so 1 = Y1/1. Conclude that the missing coordinate, Y1, is equal to 1, since, 1 = Y1 is the same as Y1 = 1.


The most common mistake in solving for missing coordinates is not entering the coordinates in the right order when you substitute the coordinates into the slope equation (mixing up the order of X1 and X2 or Y1 and Y2). This will result in a slope that has the wrong sign (a negative slope instead of a positive slope or a positive slope instead of a negative slope).

About the Author

Mark Stansberry has been a technical and business writer over for 15 years. He has been published in leading technical and business publications such as "Red Herring," "EDN" and "BCC Research." His present writing focus is on computer applications programming, graphic design automation, 3D linear perspective and fractal technology. Stansberry has a Bachelor of Science in electrical engineering from San Jose State University.