Origin in Math | Definition, Graph & Examples
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Origin in Math: Multiple Choice Exercise
This activity will help you assess your knowledge of how origin in math is used.
Directions
For this activity, carefully read and select the best answer that completes each of the given statements. To do this, print or copy this page on blank paper and circle the letter of your answer.
Multiple Choice
1.) When you move towards the left of a point, x and y become __________.
A. points of origin
B. positive numbers
C. negative numbers
D. zero
2.) Which of the following statements is TRUE about plotting the point (4,7)?
A. You move 4 units to the left from the origin.
B. You move 7 units to the right from the origin.
C. You move 7 units to the left from the origin.
D. You move 4 units to the right from the origin.
3.) The y axis represents __________.
A. The number of units that you move to the left or right from the origin.
B. The number of units that you move up from the origin.
C. The number of units that you move up or down from the origin.
D. The number of units that you move down from the origin.
4.) How many units will you have to move up from the origin to plot the point (2,-5)
A. 0 unit
B. 2 units
C. -5 units
D. 5 units
5.) How many units will you need to move down the origin to get to the point (4,-7)?
A. -7 units
B. 7 units
C. 4 units
D. 0 unit
Answer Key
1.) C
2.) D
3.) C
4.) A
5.) A
Why is (0,0) called the origin?
The Cartesian plane is defined by two number lines, each with origin at 0, which intersect at the shared point (0,0). All points in the plane can be measured according to their distance from this central point.
What is the origin on a graph?
A graph in the two-dimensional coordinate plane has the point (0,0) as its origin. The origin is located at the intersection of the vertical and horizontal axes, and the distance to all points can be measured from this point.
What is an origin in math?
An origin is a single point of reference for a coordinate system, from which all other values can be measured. Its exact definition depends on the coordinates system in use and its dimension in particular.
Table of Contents
ShowThe term "origin" is regularly used in math classes and textbooks, but what does it mean?
Whenever we use numerical values to describe the physical world, including measuring lengths with a ruler or navigating using compass headings, measurements are always given relative to some agreed point of reference. Directions to head North and West mean moving in that direction starting from your current location. In mathematical terminology, this initial reference point is known as the origin.
Point of Origin Definition
The point of origin, or simply the origin for short, is the reference point in a coordinate system from which all other measurements are taken.
A coordinate system consists of one or more variables, each of which can be measured along a number line. In particular, the two-dimensional coordinate plane consists of two number lines, which, for example, could represent directions North and South and East and West. All other points on the plane can be treated as positions relative to a single point of reference called the origin, which is often labeled with the letter {eq}O {/eq}.
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Perhaps the most familiar use of coordinate planes is for graphing functions of a single variable. If {eq}y=f(x) {/eq}, we can represent each variable, {eq}x {/eq} and {eq}y {/eq} on its own number line. To understand how the origin is found in the resulting graph, we must first understand how the origin is located on a single number line, and how precisely two number lines are used to define the coordinate plane. Let's review these ideas first.
Origin on a Number Line
A number line is a straight line with graduated markings used to represent real numbers. One point on the line must represent the number zero. By default, positive numbers are counted toward the right of zero, and negative numbers are counted toward the left.
Zero plays the role of the origin on a number line because all numbers, both positive and negative, increase in absolute value (or magnitude, meaning size) the farther they are from zero. In this way, all numbers become measurements relative to a single origin.
Constructing a Coordinate Plane Graph
A number line can be used to represent the values of a single measurement or variable. To represent two variables, we can create a coordinate plane by drawing two perpendicular number lines: a horizontal {eq}x {/eq}-axis and a vertical {eq}y {/eq}-axis. By referring to the axes, we can treat the two-dimensional plane as a grid in which any point can be identified by a coordinate pair {eq}(x, y) {/eq}. Positive and negative {eq}x {/eq} values are measured to the right and left respectively, and positive and negative {eq}y {/eq} values are measured up and down.
The coordinate plane is also known as the Cartesian plane, after the French mathematician Rene Descartes, who first conceived the idea. {eq}x {/eq} and {eq}y {/eq} are referred to as Cartesian coordinates.
The vertical and horizontal axes which create the Cartesian plane must intersect, and they are drawn so that the zero values of each coincide. The Cartesian coordinates of this single intersection point must then be {eq}(0, 0) {/eq}, and this point becomes the origin in the plane.
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