Sometimes you might be given the distance between two points on a coordinate plane, but not told the complete coordinates of one point.

Using the distance formula we can determine this missing information.

y+

x+

(-20, -45)

(20, y2)

In this example we want to figure out the value of y2.

Substitute in values for the x’s and y’s.

Simplify.

Solve for y2.

Solve for y2.

Square both sides of the equation to cancel out the square root.

Simplify.

Take the square root of both sides to get rid of the square term.

Subtract 45 from both sides of the equation.

The value of y2.

Now we have found the missing coordinate. Our coordinates are (-20, -45) and (20, 50).

You can follow this same procedure to find a missing coordinate when you know the distance between it and some other point on a coordinate plane.