Geometric Transformations and Coordinate Formulas

Vocabulary flashcards covering key coordinate geometry formulas, reflections, rotations, slopes, and midpoint form.

Slope formula

The formula used to calculate the steepness of a line between points $(x_1, y_1)$ and $(x_2, y_2)$, defined as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Reflection over x-axis

A coordinate transformation that flips a point $(x, y)$ across the x-axis to $(x, -y)$.

Reflection over y-axis

A coordinate transformation that flips a point $(x, y)$ across the y-axis to $(-x, y)$.

Reflection over y=x

A coordinate transformation that flips a point $(x, y)$ across the line $y = x$ to $(y, x)$.

Rotation 90 degrees counterclockwise

A transformation that rotates a point $(x, y)$ counterclockwise around the origin by $90^\text{o}$ to $(-y, x)$.

Rotation 180 degrees counterclockwise

A transformation that rotates a point $(x, y)$ counterclockwise around the origin by $180^\text{o}$ to $(-x, -y)$.

Rotation 270 degrees counterclockwise

A transformation that rotates a point $(x, y)$ counterclockwise around the origin by $270^\text{o}$ to $(y, -x)$.

Perpendicular slope

The slope of a line that forms a $90^\text{o}$ angle with a line of slope $m$, equal to its negative reciprocal $-\frac{1}{m}$.

Parallel slope

The slope of a line that runs parallel to another line, which is equal to the original slope $m$.

Midpoint Form

The formula for finding the center point between $(x_1, y_1)$ and $(x_2, y_2)$, given by \begin{pmatrix} \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \begin{pmatrix}.