MPM 2D Strand B-Exam Review Flashcards

Vocabulary and concepts for the MPM 2D Strand B Review, covering systems of equations, analytic geometry of line segments, and circle equations.

Point of Intersection

The coordinate where two lines cross, which satisfies both equations in a system simultaneously, such as checking if $(2, 1)$ is a solution for $x + 4y = 6$ and $2x - 3y = 7$.

Substitution Method

A method for solving a system of equations, such as $x - 2y = 5$ and $3y - 2x = 7$, by isolating one variable and substituting it into the other equation.

Elimination Method

A method for solving a system of equations, such as $3x + 2y = 2$ and $4x + 5y = 12$, by adding or subtracting equations to remove one variable.

Midpoint (M)

The point that is exactly halfway between two endpoints of a line segment, such as point $M(2, 0)$ between $A(-6, 4)$ and an unknown endpoint $B$.

Length of a Line Segment

The distance between two endpoints $A$ and $B$, calculated as an exact value using the distance formula.

Right-triangle

A triangle, such as one with vertices $X(-1, -3)$, $Y(1, -1)$, and $Z(-5, 5)$, where the slopes of two sides are negative reciprocals or the side lengths satisfy the Pythagorean theorem.

Circle Equation (Center at Origin)

An equation of the form $x^2 + y^2 = r^2$, where the center is at $(0,0)$ and $r$ is the radius.

Radius (r)

The distance from the center of a circle to its circumference; for example, in the equation $x^2 + y^2 = 64$, the radius is $\text{8}$.

Radius Calculation from a Point

The process of finding $r$ using the coordinates of a point on the circumference, such as $(-5, 12)$, and the origin $(0,0)$ using the formula $r = \text{radius} = \text{distance from origin to point}$.

y-intercepts of a Circle

The coordinates where a circle crosses the y-axis, found by setting $x = 0$ in the circle's equation.