February Winter Packet (2014) (2)
... Write ordered pairs of integers that satisfy the criteria in each part below. Remember that the origin is the whose coordinates are (0,0). When possible, give ordered pairs such that: (i) both coordinates are positiv For problems 5–7, answer true or false. If false, explain why. both coordinates are ...
... Write ordered pairs of integers that satisfy the criteria in each part below. Remember that the origin is the whose coordinates are (0,0). When possible, give ordered pairs such that: (i) both coordinates are positiv For problems 5–7, answer true or false. If false, explain why. both coordinates are ...
CC Investigation 3: Integers and the Coordinate Plane
... 67. Carlos is trying to get to a movie that starts in 45 minutes. Write an inequality that shows how long Carlos can take if he wants to make it before the start of the movie. Graph the solution. Explain your choice of an open circle or a closed circle in the graph. 68. Etta is planning a trip to Ca ...
... 67. Carlos is trying to get to a movie that starts in 45 minutes. Write an inequality that shows how long Carlos can take if he wants to make it before the start of the movie. Graph the solution. Explain your choice of an open circle or a closed circle in the graph. 68. Etta is planning a trip to Ca ...
Moore Catholic High School Math Department
... collinear points - Points that lie on the same line. complementary angles - Two angles the sum of whose measures is 90 degrees. congruent - Having the same size and shape. coordinate plane - The set of all points in a plane designated by their Cartesian coordinates (x, y). Also called the Cartesian ...
... collinear points - Points that lie on the same line. complementary angles - Two angles the sum of whose measures is 90 degrees. congruent - Having the same size and shape. coordinate plane - The set of all points in a plane designated by their Cartesian coordinates (x, y). Also called the Cartesian ...
Subject: Geometry - Currituck County Schools
... G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g. transla ...
... G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g. transla ...
Sample Geometry Projects with Scratch
... Coordinate Grids NCTM Standard In grades 6–8 all students should: 1. Specify locations and describe spatial relationships using coordinate geometry and other representational systems • use coordinate geometry to represent and examine the properties of geometric shapes; • use coordinate geometry to ...
... Coordinate Grids NCTM Standard In grades 6–8 all students should: 1. Specify locations and describe spatial relationships using coordinate geometry and other representational systems • use coordinate geometry to represent and examine the properties of geometric shapes; • use coordinate geometry to ...
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 in a plane may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.