Endpoint Math Formula

Students typically learn about the endpoint formula during an algebra class.
••• Hemera Technologies/AbleStock.com/Getty Images

Students learn how to apply the endpoint math formula -- a derivation of the midpoint formula -- during a unit on graphing in the coordinate plane, which is typically taught in an algebra course but sometimes covered in a geometry course. To use the endpoint math formula, you must already know how to solve two-step algebraic equations.

Problem Setup

Problems involving the endpoint math formula involve three points of a line segment: the two endpoints and the midpoint. You are given the midpoint and one endpoint and asked to find the other endpoint. The formula to use is a derivation of the better-known midpoint formula. Letting (m1, m2) represent the given midpoint, (x1, y1) represent the given endpoint, and (x2, y2) represent the unknown endpoint, the formula is: (x2, y2) = (2_m1 – x1, 2_m2 – y1).

Worked Example

Suppose you are given a midpoint of (1, 0), one endpoint of (-2, 3) and asked to find the other endpoint. In this example, m1 = 1, m2 = 0, x1 = -2, y1 = 3 and x2 and y2 are the unknowns. Substituting the known values into the aforementioned formula produces (x2, y2) = (2_1 – -2, 2_0 – 3). Simplify using the order of operations -- that is, first perform the multiplication, and then perform the subtraction. Doing so yields (x2, y2) = (2 – -2, 0 – 3), which then becomes (x2, y2) = (2+2, 0 – 3), resulting in a final answer of (x2, y2) = (4, -3). If you wish, you may check your solution by substituting all points into the midpoint formula: (m1, m2) = {[(x1 + x2)/2], [(y1 + y2)/2]}.

Related Articles

How to Create Linear Equations
How to Solve a Parabola
How to Find Equations of Tangent Lines
How to Find the Area of a Triangle
How to Solve Slope-Intercept Form
How to Find Y Value for the Slope of a Line
How to Find the Cotangent on a Graphing Calculator
How to Find the Vertices of an Ellipse
How to Graph and Find the Solution on a Calculator
How to Find a Missing Angle
How to Plot a Michaelis-Menten Curve
How to Calculate the Midpoint Between Two Numbers
To Calculate Arcsine, What Buttons Do You Press on...
How to Solve for a Variable in a Trig Function
How to Multiply Vectors
How to Calculate Kf
How to Find the Missing Slope of a Trapezoid
How to Find the X Factor in a Math Equation
How to Find the Vertex of a Parabola Equation
How to Calculate Correlation Coefficients With an Equation