Mathematics Review: Rational Equations, Cartesian Plane, Sequences, Distance and Midpoint

Flashcards covering key mathematical review topics including simple rational algebraic equations, Cartesian coordinate plane concepts, sequence patterns, and coordinate distance and midpoint formulas.

Simple Rational Algebraic Equation

An equation containing rational expressions that can be solved by setting two algebraic fractions equal to each other and applying cross-multiplication.

Cross-Multiplication

A procedure used to solve an equation of two equal ratios $\frac{a}{b} = \frac{c}{d}$ by setting the diagonal products equal: $a \times d = b \times c$.

Cartesian Coordinate Plane

A two-dimensional surface defined by two perpendicular number lines, the horizontal $x$-axis and vertical $y$-axis, intersecting at the origin.

Coordinate of a Point

An ordered pair of numbers $(x, y)$ representing the horizontal and vertical location of a point on the Cartesian coordinate plane.

Sequence Pattern Rule

A rule or formula identified by observing numerical patterns to determine the next term in a sequence.

Distance Between Two Points

The straight-line length between points $(x_1, y_1)$ and $(x_2, y_2)$ on the Cartesian coordinate plane, calculated using $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Midpoint of a Line Segment

The point that bisects a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$, determined using $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.