Geometry: Segment Addition, Midpoint, and Distance Formulas

Vocabulary flashcards covering core concepts, postulates, and coordinate formulas from the geometry worksheet on segment addition, midpoints, and distances.

Segment Addition Postulate

A geometric rule stating that if a point $R$ lies on a line segment $ST$ between endpoints $S$ and $T$, then the sum of the lengths of the individual segments equals the total length: $SR + RT = ST$.

Midpoint Formula (2D Coordinate Plane)

The formula used to find the coordinates of the midpoint $M$ between two points $(x_1, y_1)$ and $(x_2, y_2)$: M = \begin{pmatrix} \frac{x_1 + x_2}{2}, & \frac{y_1 + y_2}{2} \begin{pmatrix}.

Distance Formula

An algebraic formula derived from the Pythagorean theorem used to calculate the distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane: d = \root{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Midpoint Formula (1D Number Line)

The formula used to determine the midpoint coordinate $M$ between two endpoints $a$ and $b$ on a single-variable number line: $M = \frac{a + b}{2}$.

Midpoint

The exact middle point on a line segment that bisects it into two congruent segments of equal length.

Numerical Length of a Segment

The positive real numerical value representing the total distance between the two endpoints of a given line segment.