Posts Tagged ‘points’
Thursday, December 24th, 2009
Finding the Function of a Directed Graph
Description
A detailed tutorial on finding the function of a directed graph. Step by step tutorial including several examples of finding functions of digraphs for reference.
Overview
A directed graph, more commonly known as a digraph, is the visual representation of a function or of a relation. As in any graph, there are points and lines – called vertices and edges in a digraph. Each edge has an arrow pointing to a vertex. The first vertex – the one the arrow comes from – is the x coordinate of an ordered pair. The second vertex – the one the arrow is pointing to – is the y coordinate of an ordered pair. In the case of double-sided arrows, two ordered pairs are made, with the x and y coordinates switching. This is done for every single vertex and edge on the graph.
Tags: arrow, coordinate. ordered, digraph, directed, discrete math, double, edges, expression, First, function, graph, lines, pair, points, relation, representation, second, side, vertex, vertices, visual, x, y
Posted in Discrete Math | No Comments »
Tuesday, November 17th, 2009
Introduction to Half-Planes
Description
A detailed tutorial on half-planes. Step by step tutorial including several examples of half-planes for reference.
Overview
A half-plane is simply half a plane, that includes all the lines on half of the plane and sometimes the points. If the plane includes the points, it is a closed half-plane. If it doesn’t, then it is an open half-plane. The most common half planes are upper, lower, right, and left planes, where that side of the plane is all that is included. However, there are many other kinds of half planes that are all a variety of diagonal half-planes.
Tags: bottom, closed, Geometry, half, half-plane, left, lines, lower, open, plane, points, region, right, top, upper
Posted in Geometry | No Comments »
Tuesday, November 17th, 2009
How to Draw a Boundary Line
Description
A detailed tutorial on how to draw a boundary line. Step by step tutorial including several examples on how to draw a boundary line for reference.
Overview
A boundary line is used when graphing inequalities on a number line or a regular Cartesian graphing system. What the boundary line does is connect the two points in the inequality – in other words, it sets a boundary of what an unknown variable would be on that inequality. The boundary line can either be solid or dashed. The boundary line is only dashed when it is drawn on a regular graph, to express that the line was somewhere else at one point and was then moved. In all other cases, the boundary line is solid.
Tags: algebra, boundary, closed, coordinates, dashed, equal, graph, greater, inequality, interval, less, line, number, open, points, solid, then, to
Posted in Algebra | No Comments »
Thursday, November 12th, 2009
How to Draw Best-Fitting Lines
Description
A detailed tutorial on how to draw best-fitting lines. Step by step tutorial including several examples on how to draw best-fitting lines for reference.
Overview
Best-fitting lines are lines that are drawn on a graph or on scatter plots. However, a best-fitting line is different than a normal line found on a graph. A normal graph simply requires you to connect the dots. A best fitting line focuses not on what dots to connect, but how to connect them. The line will curve or go in different directions, not just straight to the other line, depending on the relationship of the two dots to each other. Best-fitting lines typically require more information than simply the graph, you must explore the equation and each point to find the true relationships, and from that you can find the best-fitting line.
Tags: algebra, best, best-fitting, connect, coordinate, curve, direction, dots, equation, fitting, graph, line, plot, points, relationship, scatter, straight
Posted in Algebra | No Comments »
Thursday, October 15th, 2009
How to Find the Directrix of a Parabola
Description
A detailed tutorial on how to find the directrix of a parabola. Step by step tutorial including several examples of how to find the directrix of a parabola for reference.
Overview
A parabola is a curved shape that is formed by the graph of the function x squared. A parabola is technically known as the locus of points where the distance to the focus equals the distance to the directrix. The directrix is a given line on a parabola that does not go through the focus.
Tags: algebra, curve, directrix, focus, function, graph, line, locus, Math, parabola, points, squared, x
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
Plotting Points in the Polar Coordinate System
Description
A detailed tutorial on plotting points in the polar coordinate system. Step by step tutorial including several examples of how to plot points on the polar coordinate system for reference.
Overview
By this point, everyone should know how to plot points on a normal graph. But what about a circular graph? This circular graph is called the polar coordinate system or the polar plane. Instead of using the points (x, y), the polar coordinate system uses the points (r, theta). Theta is a greek letter that looks like a zero with a horizontal line drawn through the center. Most of the points you will be finding for the polar coordinate system will be used with trigonometric functions – sine, cosine, and tangent. Graphing occurs in about the same way as it would on a normal graph – just match up the points, even if they are on a circle.
Tags: Calculus, circle, coordinate, cosine, function, functions, graph, Math, points, polar, r, sine, system, tangent, theta, trig, trigonometric, x, y
Posted in Calculus | No Comments »
Friday, October 2nd, 2009
Introduction to Scatter Plots
Description
A detailed tutorial on scatter plots. Step by step tutorial including several examples of scatter plots for reference.
Overview
A scatter plot is more of a diagram than a graph. but it uses Cartesian coordinates to display the values in a set of data. A scatter plot is normally defined as a collection of points – it is almost like a regular Cartesian graph, but the points are not connected and there are typically more of them. Scatter plots can also be 3D.
Tags: algebra, cartesian, collection, coordinates, horizontal, Math, points, scatter chart, scatter diagram, scatter graph, scatter plot, values, vertical
Posted in Algebra | No Comments »
Friday, September 11th, 2009
How to Find the Equation of a Circle
Description
A detailed tutorial on how to find the equation of a circle. Step by step tutorial including several examples of how to find the equation of a circle for reference.
Overview
The equation of a circle is really the distance from the point (h, k) – the center of the circle – to the point (x, y) – a point somewhere on the outside of the circle. This distance will be called r. Having this information, we can now insert it into the distance formula:
r = sqrt[(x - h)^2 + (y - k)^2]
But because no one wants to solve a square root, we can simplify the formula and get rid of the square root entirely:
r^2 = (x – h)^2 + (y – k)^2
This is the general formula for a circle. You must always have the center and radius of a circle to be able to solve. However, even if you are not given these you can easily find them by using the distance and midpoint formulas with whatever points you are given.
Tags: algebra, center, circle, distance formula, equation, equation of a circle, Geometry, Math, midpoint, Outside, points, radius
Posted in Algebra | No Comments »
Thursday, September 3rd, 2009
How to Find the Midpoint
Description
This video gives one example of how to use the midpoint formula when given two (x, y) points. Tips for solving are included in the video. This video provides a more complicated example to show that midpoint is not impossible to find when given more complicated numbers.
Overview
The midpoint formula is similar to the distance formula because it used for lines and graphs. Very often the two formulas are used together. The midpoint formula is not so much a formula as a point on the line that you must solve for. The formula is ({x1 + x2}/2 , {y1 + y2}/2). In order to use this formula, you must be given two points on a graph: (x1, y1) and (x2, y2). Plug these in their proper place in the formula and solve the equations. You should end up with another (x, y) point. This is your midpoint – the point right in the middle of these two points you were given.
Tags: algebra, Geometry, graphs, lines, Math, midpoint, midpoint formula, points
Posted in Algebra | No Comments »
Thursday, September 3rd, 2009
How to Find the Distance Between Two Points
Description
This video shows how to solve one distance formula problem, with a “solve it yourself” option available. It provides a clear method of solving and easy explanations. The steps are laid out in an easy to follow method.
Overview
Distance is a very common formula in geometry. The formula that is used to solve distance is d = sqrt[(x2 - x1)^2 - (y2 - y1)^2]. In order to use the distance formula, you must be given two points on a graph, represented as (x1, y1) and (x2, y2). You then must plug them in the appropriate places on the distance formula. Continue to solve as you would any basic algebra problem, using the order of operations.
Tags: distance, distance formula, Geometry, graphs, lines, Math, points
Posted in Geometry | 1 Comment »
