Formula Quiz Study Guide Flashcards

Vocabulary flashcards covering core algebra and geometry formulas from the study guide, including line segment solving, midpoint, distance, slope equations, and reflection rules.

Line Segment Relationships

Formulas used to solve line segment lengths: $\text{Part} + \text{Part} = \text{Whole}$ or $\text{Part} = \text{Part}$.

Distance Formula

Formula to find the distance between two points: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Midpoint Formula

Formula to determine the midpoint coordinates of a segment: $MP_{(x, y)} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Midpoint X-Value

Formula to calculate the x-coordinate of the midpoint: $MP_x = \frac{x_1 + x_2}{2}$.

Midpoint Y-Value

Formula to calculate the y-coordinate of the midpoint: $MP_y = \frac{y_1 + y_2}{2}$.

Partitioning a Segment

Formula to partition a line segment given ratio scale factor $k$: $\left[k(x_2 - x_1) + x_1, k(y_2 - y_1) + y_1\right]$.

Slope

Formula for calculating the slope $m$ between two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Slope-Intercept Form

Linear equation expressed as $y = mx + b$.

Standard Form

Linear equation expressed as $Ax + By = C$.

Point-Slope Formula

Linear equation form given a point and a slope: $y - y_1 = m(x - x_1)$.

Reflecting over the line $y = x$

Geometric transformation rule where you flip $x$ and $y$ coordinates.

Reflecting over the line $y = -x$

Geometric transformation rule where you flip $x$ and $y$ coordinates and change their signs.