Name: finding points on the coordinate plane
Uploaded: 2025-11-26T05:44:24.000Z
Duration: 1 min 21 s
Channel: JoVE

El plano de coordenadas, o plano cartesiano, está formado por dos rectas numéricas perpendiculares: un eje x horizontal y un eje y vertical.Estos ejes se cruzan en el origen, el punto donde ambos valores son cero, dividiendo el plano en cuatro cuadrantes etiquetados.Un par ordenado de coordenadas representa todas las ubicaciones del plano. El primer número indica la posición a lo largo del eje x y el segundo muestra la posición en el eje y.Las coordenadas funcionan como un sistema de direcciones, identificando de forma única cada punto del plano.Por ejemplo, un punto con las coordenadas (2, 3) se encuentra dos unidades a la derecha y tres unidades por encima del origen.Todos los puntos con valores x positivos se encuentran a la derecha del eje y, y aquellos con valores x negativos se encuentran a la izquierda. Una línea horizontal representa puntos que comparten el mismo valor de y, y una línea vertical muestra puntos con el mismo valor de x, ya sea positivo o negativo.El sistema de coordenadas tiene aplicaciones en el mundo real. Por ejemplo, los drones dependen de él para seguir rutas de vuelo precisas y llegar a lugares específicos.

plano de coordenadas

El plano de coordenadas cartesianas es una estructura fundamental en la matem&#225;tica que permite visualizar las relaciones entre valores num&#233;ricos en dos dimensiones. Est&#225; formado por dos ejes num&#233;ricos que se intersectan: un eje x horizontal y un eje y vertical. Estos ejes se encuentran en el origen, el punto donde ambos valores son cero. Su intersecci&#243;n divide el plano en cuatro cuadrantes, etiquetados en sentido contrario a las agujas del reloj comenzando desde el cuadrante superior derecho.
Un par ordenado de n&#250;meros representa cada punto en el plano de coordenadas. El primer n&#250;mero, la coordenada x, indica la posici&#243;n a lo largo del eje horizontal, mientras que el segundo n&#250;mero, la coordenada y, indica la posici&#243;n a lo largo del eje vertical. Estas coordenadas act&#250;an como un sistema de localizaci&#243;n, especificando de forma &#250;nica la ubicaci&#243;n de cada punto. Por ejemplo, el punto con coordenadas (2, 3) se encuentra dos unidades a la derecha y tres unidades por encima del origen, ubicado en el primer cuadrante. Los valores negativos de x colocan los puntos a la izquierda del eje vertical, mientras que los negativos de y los sit&#250;an por debajo del eje horizontal.
Los puntos que comparten el mismo valor de y se sit&#250;an a lo largo de una l&#237;nea horizontal, y aquellos con el mismo valor de x se sit&#250;an a lo largo de una l&#237;nea vertical. Estas l&#237;neas tambi&#233;n pueden servir como l&#237;mites, que definen regiones espec&#237;ficas del plano. Por ejemplo, todos los puntos entre dos l&#237;neas horizontales forman una banda horizontal, mientras que una banda vertical se forma entre dos l&#237;neas verticales.
Este sistema traza puntos individuales, construye formas geom&#233;tricas y analiza datos. Proporciona una base para diversas aplicaciones en la matem&#225;tica, la ciencia y la tecnolog&#237;a, donde la representaci&#243;n espacial y la precisi&#243;n son esenciales.

Plano de coordenadas

El plano de coordenadas cartesianas es una estructura fundamental en la matem&#225;tica que permite visualizar las relaciones entre valores num&#233;ricos ...

Education

Educación

JoVE Core

Math Fundamentals

Fundamentos de matemáticas

Unit

Unidad

Coordinates and Graphs

Coordenadas y gráficas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Coordinate Plane

finding points on the coordinate plane

The Cartesian coordinate plane is used to find and plot points in two dimensions. It is made of two number lines that cross at right angles. The horizontal line is the x-axis, and the vertical line is the y-axis. Their meeting point is the origin, where both values are zero.

The axes divide the plane into four quadrants. These quadrants are labeled in a counterclockwise direction, starting from the upper right. Every point on the plane is written as an ordered pair. The first number is the x-coordinate, and it shows position along the horizontal axis. The second number is the y-coordinate, and it shows position along the vertical axis.

Ordered pairs work like an address system for the plane. For example, the point (2, 3) is two units to the right and three units above the origin. That point lies in the first quadrant. Negative x-values place points to the left of the vertical axis, and negative y-values place points below the horizontal axis.

Points with the same y-value lie on a horizontal line. Points with the same x-value lie on a vertical line. These lines can also mark boundaries for regions of the plane. A horizontal strip forms between two horizontal lines, and a vertical strip forms between two vertical lines.

The coordinate plane is useful for plotting individual points, building geometric shapes, and analyzing data. It gives a precise way to show relationships between numbers. This makes it important in mathematics, science, and technology, where clear spatial representation matters.

Finding Points on the Coordinate Plane

coordinate plane

The Cartesian coordinate plane is used to find and plot points in two dimensions. It is made of two number lines that cross at right angles. The horizontal line is the x-axis, and the vertical line is the y-axis. Their meeting point is the origin, where both values are zero. The axes divide the plane into four quadrants. These quadrants are labeled in a counterclockwise direction, starting from the upper right. Every point on the plane is written as an ordered pair. The first number is the...

the distance formula

Finding Distance on a Coordinate Plane

Finding distance on a coordinate plane uses the distance formula and the Pythagorean Theorem. In geometry, this method helps measure the direct distance between two points on a flat plane. It is useful in many practical and theoretical settings. The formula comes from a right triangle. On a coordinate plane, the horizontal and vertical differences between two points become the legs of that triangle. The line connecting the points is the hypotenuse, and that is the shortest path between them. <br...

the midpoint formula

Finding the Center of a Line Segment

Finding the center of a line segment is a key idea in coordinate geometry. The midpoint is the point that lies exactly halfway between two points on a coordinate plane. It is used in mathematics, physics, engineering, and planning work where a central location matters. To work with a midpoint, start with two points, A(x1, y1) and B(x2, y2). A straight line segment can be drawn between them on the coordinate plane. The midpoint, labeled M, divides that segment into two equal parts. The...

graphs of equations in two variables

Plotting Two-Variable Equations with Tables

Plotting two-variable equations with tables helps show how x and y are related. An equation written as y = f(x) or Ax + By = C gives ordered pairs that satisfy the rule. Each pair can be checked by substituting the x and y values into the equation. A value table is a common way to build the graph. Start by choosing several values for the independent variable x. Then substitute each x value into the equation to find the matching y value. The results become ordered pairs on the Cartesian...

circles

Circle Equations in Standard Form

Circle equations in the coordinate plane use a center and a radius to describe every point on the curve. A circle is the set of all points that stay the same distance from a fixed point called the center. That constant distance is the radius. The distance formula connects a point x, y on the circle to the center h, k. The distance between those two points equals the radius r. When both sides of the distance formula are squared, the equation of the circle can be written in standard form. <br...

symmetry

Ellipse Symmetry at the Origin

An ellipse centered at the origin shows clear symmetry in its graph. Its equation describes a smooth, closed curve whose distance from the center keeps a constant ratio between the horizontal and vertical axes. Because the ellipse stretches farther along the x-axis than the y-axis, it has a horizontal shape. This ellipse has symmetry across the x-axis. That means the top half and bottom half are mirror images across the horizontal axis. Algebraically, the equation stays the same when y is...

solving equations graphically

Graphing Equations to Find Intercepts

Graphing equations helps students find intercepts and solutions on the coordinate plane. It gives a visual way to solve equations and understand how a function behaves. To use this method, write the equation in the form y = f(x). The solution to the original equation is the x-value where the graph crosses the x-axis. At that point, f(x) = 0. For example, the linear equation 2x - 4 = 0 can be written as y = 2x - 4. When this function is graphed, it has one x-intercept at x = 2, and that is the...

solving inequalities graphically

Graphing Inequality Solution Ranges

Graphing inequality solution ranges gives a visual way to find the x-values that make an inequality true. Students look at where a graph sits compared with the x-axis or with another graph. This shows the interval where the condition is satisfied. For a quadratic inequality, the first step is to plot the related function. For example, with x² − 4x + 2 &lt; 0, graph y = x² − 4x + 2. The solution is the set of x-values where the curve lies below the x-axis. Inequalities can also compare two...

key terms and concepts

Learn how the Cartesian coordinate plane uses the x-axis, y-axis, quadrants, and ordered pairs to plot points, draw shapes, and show data clearly.

Finding Points on the Coordinate Plane | JoVE K12

The JoVE Math Fundamentals collection is designed to build a deep and comprehensive understanding of essential mathematics. Covering the foundations of algebra, geometry, trigonometry, and analytic reasoning, this course establishes a strong base for future studies. The collection connects core mathematical concepts with real-world practice, equipping learners to solve complex problems, master problem-solving skills, and apply abstract ideas.

math fundamentals

Finding Points on the Coordinate Plane

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