Enhance Your Learning with Coordinate Geometry Flash Cards for quick learning
A location in space, represented by an ordered pair (x, y) in a coordinate plane.
A straight path that extends infinitely in both directions, represented by an equation or two points on the line.
The measure of the steepness of a line, calculated as the change in y-coordinates divided by the change in x-coordinates.
A formula used to find the distance between two points in a coordinate plane, given by sqrt((x2 - x1)^2 + (y2 - y1)^2).
A formula used to find the midpoint between two points in a coordinate plane, given by ((x1 + x2) / 2, (y1 + y2) / 2).
Lines in a plane that never intersect, having the same slope.
Lines in a plane that intersect at a right angle, having negative reciprocal slopes.
An equation that represents a line in a coordinate plane, typically in the form y = mx + b, where m is the slope and b is the y-intercept.
The process of plotting points and connecting them to form a line that represents the solution set of a linear equation.
Operations that change the position, size, or shape of a figure, including translations, reflections, rotations, and dilations.
Curves formed by the intersection of a plane and a cone, including circles, ellipses, parabolas, and hyperbolas.
A quantity that has both magnitude and direction, represented by an ordered pair (a, b) or a directed line segment.
A coordinate system in which each point is determined by its distance from the origin and the angle it forms with the positive x-axis.
A set of equations that express the coordinates of a point as functions of one or more independent variables, typically representing a curve or surface.
The study of geometry in three dimensions, using coordinates (x, y, z) to represent points in space.
One of the four regions into which the coordinate plane is divided by the x-axis and y-axis.
The point (0, 0) where the x-axis and y-axis intersect in a coordinate plane.
The horizontal number line in a coordinate plane.
The vertical number line in a coordinate plane.
A system of coordinates in which the position of a point is determined by its distance from two perpendicular lines, the x-axis and y-axis.
A pair of numbers (x, y) that represents the coordinates of a point in a coordinate plane.
The point or points where two or more lines or curves meet or cross.
Lines that are always the same distance apart and never intersect.
Lines that intersect at a right angle.
The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
The equation of a line in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
The equation of a line in the form Ax + By = C, where A, B, and C are constants and A and B are not both zero.
A line that is parallel to the y-axis and has an undefined slope.
A line that is parallel to the x-axis and has a slope of zero.
A transformation that moves every point of a figure the same distance in the same direction.
A transformation that flips a figure over a line, creating a mirror image.
A transformation that turns a figure around a fixed point called the center of rotation.
A transformation that changes the size of a figure, either making it larger or smaller.
A conic section formed by the set of all points in a plane that are equidistant from a fixed center point.
A conic section formed by the set of all points in a plane for which the sum of the distances to two fixed points is constant.
A conic section formed by the set of all points in a plane that are equidistant from a fixed point (focus) and a fixed line (directrix).
A conic section formed by the set of all points in a plane for which the difference of the distances to two fixed points is constant.
The size or length of a vector, represented by the absolute value or modulus of the vector.
The angle or orientation of a vector, represented by the direction of the vector or the angle it forms with a reference line.
A vector that starts at the origin (0, 0) and ends at a given point (a, b).
A vector with a magnitude of 1, used to represent direction.
A quantity that has magnitude but no direction, represented by a single number.
The reference line in a polar coordinate system, usually the positive x-axis.
The angle formed between the polar axis and the line segment connecting the origin to a point in a polar coordinate system.
The distance from the origin to a point in a polar coordinate system, represented by the length of the line segment connecting them.
A curve defined by a set of parametric equations, where the coordinates of a point on the curve are given as functions of a parameter.
A set of parametric equations that represent a line in a coordinate plane, typically in the form x = at + b, y = ct + d, where t is the parameter.
The first value in an ordered pair (x, y), representing the horizontal position of a point in a coordinate plane.
The second value in an ordered pair (x, y), representing the vertical position of a point in a coordinate plane.
The third value in an ordered triple (x, y, z), representing the position of a point in three-dimensional space.
A space that has three dimensions: length, width, and height, represented by the x-axis, y-axis, and z-axis.