Coordinate Geometry, Quadrilateral Properties, and Conservation of Momentum

Comprehensive practice flashcards covering coordinate geometry methods, quadrilateral properties (parallelograms, trapezoids, rhombuses, squares), and classical linear momentum conservation, collisions, and impulse.

Bounding Box Method (Coordinate Area)

A coordinate geometry technique for finding the area of an irregular polygon by calculating the total area of an enclosing rectangle ($L \times W$) and subtracting the areas of outer right triangles ($\frac{1}{2}bh$) and outer rectangles.

Perimeter on a Coordinate Plane

The total boundary length of a coordinate polygon, found by calculating each side length using the distance formula ($\sqrt{(\Delta x)^2 + (\Delta y)^2}$) and summing them together.

Midpoint Formula

The coordinate geometry formula used to find the center point equidistant from two endpoints $(x_1, y_1)$ and $(x_2, y_2)$: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Point-Slope Form

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

Slopes of Perpendicular Lines

Two intersecting lines forming right angles whose slopes are negative reciprocals of one another, satisfying $m_1 \times m_2 = -1$ (e.g., a line with slope $3$ has a perpendicular slope of $-\frac{1}{3}$).

Slopes of Parallel Lines

Coplanar lines that never intersect and have identical slopes ($m_1 = m_2$).

Consecutive Angles of a Parallelogram

Adjacent interior angles along the same side of a parallelogram that are supplementary and sum to $180^\circ$.

Opposite Angles of a Parallelogram

Non-adjacent angles located across from each other in a parallelogram that are always congruent ($\cong$).

Diagonals of a Parallelogram

Segments connecting opposite non-consecutive vertices of a parallelogram that always bisect each other into equal halves.

Trapezoid

A quadrilateral having exactly one pair of parallel opposite sides, referred to as the bases.

Median of a Trapezoid

The segment connecting the midpoints of the non-parallel legs of a trapezoid, whose length equals the average of the upper and lower bases: $\frac{\text{base}_1 + \text{base}_2}{2}$.

Isosceles Trapezoid

A specific trapezoid in which the non-parallel legs are congruent ($\cong$), diagonals are congruent ($\cong$), base angles are congruent ($\cong$), and opposite angles are supplementary ($180^\circ$).

Right Trapezoid

A trapezoid that contains exactly two right angles ($90^\circ$) formed between one perpendicular leg and the two parallel bases.

Rhombus

An equilateral parallelogram having four congruent sides ($\cong$) whose diagonals are perpendicular ($\perp$) and bisect the vertex angles.

Diagonals of a Rhombus Property

Diagonals that intersect at right angles ($90^\circ$) to divide the rhombus into four congruent right triangles, allowing side lengths to be computed using the Pythagorean theorem ($a^2 + b^2 = c^2$).

Square

A regular quadrilateral possessing four congruent sides ($\cong$), four right angles ($90^\circ$), and congruent diagonals that bisect each other perpendicularly.

Law of Conservation of Momentum

The physical law stating that the total momentum of an isolated system remains constant ($p_{\text{before}} = p_{\text{after}}$) unless an external force acts on the system.

System (Physics)

The specific object or collection of interacting objects chosen for analysis in a physical scenario.

Net External Force (Momentum)

An outside force acting on a system, which serves as the sole mechanism capable of changing the total velocity and overall momentum of that system.

Scalar Nature of Mass

The principle that mass is strictly a scalar quantity and must always be positive ($m > 0$), even when an object's velocity and momentum have negative signs indicating direction.

Elastic Collision

A collision type (exemplified by polished steel spheres) in which both total system momentum and total kinetic energy are conserved ($KE_{\text{before}} = KE_{\text{after}}$).

Inelastic Collision

A collision (exemplified by soft polymer bumpers) where total system momentum is conserved, but total kinetic energy decreases ($KE_{\text{after}} < KE_{\text{before}}$) due to deformation or energy conversion.

Perfectly Inelastic Collision

An impact where colliding bodies lock or stick together (such as magnetic connectors or locking mechanisms) and travel together with a single common final velocity ($v_f$).

Push-Apart / Explosion Event

An event where two or more objects start together (often at rest with $p_{\text{initial}} = 0\,\text{kg}\cdot\text{m/s}$) and push apart via internal forces, giving each object equal and opposite momentum changes ($\Delta p_1 = -\Delta p_2$).

Impulse from a Force-Time Graph

The change in momentum ($J$), calculated as the geometric area under a force-time pulse using $J = \frac{1}{2} \times \text{base} \times \text{peak force}$.

Internal Forces in Collisions

Action-reaction forces that colliding objects exert directly on one another; because they cancel in pairs, they do not change the total system momentum.