Math L3&4 Coordinate Geometry

Vocabulary flashcards for Coordinate Geometry

Coordinate Plane

A coordinate plane comprises 2 lines, a horizontal x-axis and a vertical y-axis, perpendicular to each other, intersecting at the origin O.

Origin

The point at which the x-axis and y-axis intersect, denoted as O.

X-axis

The horizontal line in a coordinate plane.

Y-axis

The vertical line in a coordinate plane.

Quadrants

The four regions into which the coordinate plane is divided by the x and y axes.

Coordinates

Ordered pair (x, y) that represents the location of a point in the coordinate plane.

Distance Formula

A formula to calculate the distance between two points P(x1, y1) and Q(x2, y2): d = √((x2 − x1)² + (y2 − y1)²)

Midpoint Formula

The point M that divides the line segment joining two points A (x1, y1) and B (x2, y2) into two equal parts: M = ((x1 + x2)/2, (y1 + y2)/2)

Gradient (Slope)

Measure of the steepness of a line, calculated as the change in y divided by the change in x: m = (y2 − y1) / (x2 − x1)

Collinear Points

Points that lie on the same straight line.

Perpendicular Bisector

A line that bisects a line segment into two equal parts and intersects it at a right angle (90 degrees).

Point-Slope Form

y - y1 = m(x - x1)

Slope-Intercept Form

y = mx + c

Standard Form of a Line

Equation of a line expressed as ax + by = c, where a, b, and c are constants.

Intercept Form of a Line

Equation of a line expressed as x/a + y/b = 1, where a and b are the x and y intercepts, respectively.

Systems of Linear Inequalities

A set of two or more linear inequalities.

Area of a Triangle in Coordinate Plane

A formula for calculating the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3): A = 1/2 |x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|