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

Il piano delle coordinate, o piano cartesiano, è formato da due linee numeriche perpendicolari: un asse x orizzontale e un asse y verticale.Questi assi si intersecano in corrispondenza dell'origine, ovvero il punto in cui entrambi i valori sono zero, dividendo il piano in quattro quadranti etichettati.Una coppia ordinata di coordinate rappresenta ogni posizione nel piano. Il primo numero indica la posizione lungo l'asse x, mentre il secondo mostra la posizione sull'asse y.Le coordinate funzionano come un sistema di indirizzi, identificando in modo univoco ogni punto del piano.Ad esempio, un punto con le coordinate (2, 3) si trova due unità a destra e tre unità sopra l'origine.Tutti i punti con valori x positivi si trovano a destra dell'asse y e quelli con valori x negativi si trovano a sinistra. Una linea orizzontale rappresenta i punti che condividono lo stesso valore y, mentre una linea verticale mostra i punti con lo stesso valore x, sia positivo che negativo.Il sistema di coordinate ha applicazioni nel mondo reale. Ad esempio, i droni si affidano ad esso per seguire percorsi di volo precisi e raggiungere luoghi specifici.

piano cartesiano

Il piano cartesiano &#232; una struttura fondamentale in matematica che consente di visualizzare le relazioni tra valori numerici in due dimensioni. &#200; formato da due assi che si intersecano: l'asse orizzontale x e l'asse verticale y. Questi assi si incontrano all'origine, il punto in cui entrambi i valori sono pari a zero. La loro intersezione divide il piano in quattro quadranti, numerati in senso antiorario a partire dal quadrante in alto a destra.
Ogni punto sul piano cartesiano &#232; rappresentato da una coppia ordinata di numeri. Il primo numero, la coordinata x, indica la posizione lungo l'asse orizzontale, mentre il secondo numero, la coordinata y, indica la posizione lungo l'asse verticale. Queste coordinate funzionano come un sistema di indirizzi, specificando in modo univoco la posizione di ciascun punto. Ad esempio, il punto con coordinate (2, 3) si trova due unit&#224; a destra e tre unit&#224; al di sopra dell'origine, nel primo quadrante. I valori negativi di x collocano i punti a sinistra dell'asse verticale, mentre i valori negativi di y li collocano sotto l'asse orizzontale.
I punti che condividono lo stesso valore di y giacciono su una retta orizzontale, mentre quelli con lo stesso valore di x giacciono su una retta verticale. Queste rette possono anche fungere da confini, definendo regioni specifiche del piano. Ad esempio, tutti i punti tra due rette orizzontali formano una striscia orizzontale, mentre una striscia verticale si forma tra due rette verticali.
Questo sistema consente di tracciare singoli punti, costruire forme geometriche e analizzare i dati. Costituisce un fondamento per numerose applicazioni in matematica, nelle scienze e nella tecnologia, in cui la rappresentazione spaziale e la precisione sono essenziali.

Piano cartesiano

Il piano cartesiano &#232; una struttura fondamentale in matematica che consente di visualizzare le relazioni tra valori numerici in due dimensioni. ...

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Math Fundamentals

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Coordinates and Graphs

Coordinate e Grafici

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TERMINI E CONCETTI CHIAVE

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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