Midpoint formula

Learning Objectives Define the midpoint of a line segment in the context of a coordinate plane. State and correctly write the midpoint formula. Calculate the coordinates of the midpoint of a line segment given the coordinates of its two endpoints. Determine the coordinates of an unknown endpoint of a line segment when given the coordinates of the midpoint and the other endpoint. Apply the midpoint formula to solve problems involving geometric figures such as triangles, parallelograms, and circles. Use the midpoint formula as a tool in coordinate geometry proofs, such as proving that the diagonals of a parallelogram bisect each other. Ever tried to meet a friend exactly halfway between your houses? The midpoint formula is the GPS for your geometry problems! 🗺️ In this tutori...

TermDefinitionExample Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis.The grid system on a map where locations are identified by latitude and longitude. Line SegmentA part of a line that is bounded by two distinct points, called endpoints.The straight path between point A(1, 2) and point B(5, 6). EndpointsThe points at the beginning and end of a line segment.For the segment AB, the endpoints are A and B. MidpointThe point on a line segment that divides it into two equal, congruent segments.If M is the midpoint of segment AB, then the length of AM is equal to the length of MB. Ordered Pair (x, y)A pair of numbers that represents the coordinates of a point on the coordinate plane, where 'x&#...

The Midpoint Formula M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) Use this formula to find the coordinates of the midpoint (M) of a segment with endpoints (x₁, y₁) and (x₂, y₂). It finds the average of the x-coordinates and the average of the y-coordinates. Finding a Missing Endpoint Formula x_2 = 2x_m - x_1 \quad \text{and} \quad y_2 = 2y_m - y_1 Use this rearranged version of the formula when you know the midpoint (x_m, y_m) and one endpoint (x₁, y₁), and you need to find the other endpoint (x₂, y₂).