MDM2D Unit 2: Analytic Geometry

Practice vocabulary flashcards covering key formulas, classifications, and concepts from the MDM2D Analytic Geometry unit test.

Slope Formula

The formula used to determine the slope of a line segment passing through two points $(x_1, y_1)$ and $(x_2, y_2)$: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Midpoint Formula

The formula used to calculate the coordinates of the midpoint $M$ between endpoints $(x_1, y_1)$ and $(x_2, y_2)$: $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Length Formula

The formula derived from the Pythagorean theorem to calculate the distance or length $l$ of a line segment: $l = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Point-Slope Form

The linear relation formula written as $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a known point on the line.

Slope-Intercept Form

The equation of a straight line expressed as $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

Standard Form of a Linear Equation

A linear equation written in the form $Ax + By + C = 0$ (or $Ax + By = C$), where all coefficients are rearranged with integer values.

Negative Reciprocal Slopes

The property of two perpendicular lines whose slopes multiply to $-1$, defined by the relationship $m_{\perp} = -\frac{1}{m}$.

Undefined Slope

The slope of a vertical line where the change in $x$ is zero ($\Delta x = 0$), yielding an equation of the form $x = c$.

Scalene Triangle

A triangle classified by its side lengths where all three sides have different lengths and none are equal.

Right Triangle (Analytic Geometry)

A triangle containing a $90^\circ$ angle, confirmed analytically when the slopes of two intersecting sides are negative reciprocals of each other.

Altitude of a Triangle

A line (also known as the height) that joins a vertex of a triangle to its opposite side and is perpendicular to that opposite side.

Equation of a Circle

The standard algebraic form of a circle given by $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ represents the centre coordinates and $r$ is the radius.

Centre of a Circle

The central point $(h, k)$ of a circle, which corresponds to the midpoint of the circle's diameter.

Radius of a Circle

The distance or length between the centre of the circle and any point along the outside circumference of the circle.