Plotting Points in the Cartesian Plane In Exercises 6, plot the points in the Cartesian plane. (

Plotting Points in the Cartesian Plane In Exercises 6, plot...

Key Concepts

Quadrants

The Cartesian plane is divided into four regions, known as quadrants, each determined by the signs of the x and y coordinates. Recognizing these quadrants helps in understanding the spatial distribution of points and is critical in solving problems that involve coordinate geometry.

Plotting Points

Plotting points involves marking specific locations on the Cartesian plane based on their ordered pairs. Understanding how to interpret and place these coordinates on the graph is a fundamental skill in graphing, enabling visual representation of data and mathematical relationships.

Ordered Pairs

Ordered pairs, written as (x, y), represent the coordinates of a point on the Cartesian plane. The first number indicates the position along the x-axis, while the second number indicates the position along the y-axis. This notation is essential to precisely specify points in two-dimensional space.

Cartesian Coordinate System

The Cartesian coordinate system is a two-dimensional plane defined by two perpendicular number lines: the horizontal x-axis and vertical y-axis. It provides a framework for locating points using pairs of numerical coordinates, and it is foundational for graphing functions and analyzing spatial relationships.

Transcript

00:01 We are given a set of points, and we are asked to plot these points in the cartesian plane.

00:10 So the points are 1, negative 1 3 .5, negative 1, 3 7ths, 3, negative 4 thirds, negative 3 7ths, and negative 2 .5.

00:29 So in order to plot these points in the cartesian plane, first we're going to draw the cartesian.

00:35 Cartesian plane, and we're going to draw it with scales on the axes, which will make it easy to plot these points.

00:46 And then we're going to actually plot the points using the x and y components of the points.

00:57 So first we draw our cartesian plane.

01:00 This is our x ,y plane, and we see that all of our points, the x components are between, between negative 2 and positive 1.

01:23 So i'll just draw from x equals negative 2 to positive 2.

01:31 So we have our x and y axes here.

01:40 We have our origin where the axes intersect and then we have x equals negative 1, x equals negative 2 here, x equals positive 1 and x equals positive 2.

01:52 And these notches are equally spaced on the x axis.

01:57 Then looking at the y components of our points, we see that these range from negative 1 up to positive 3.

02:11 And so we're going to change our scale on the y -axis a little bit.

02:16 So we'll still make notches.

02:23 So we'll have 1, 2, 3, and these notches will be equally spaced on the y -axis.

02:31 However, now the spacing between the notches is smaller in order to accommodate our picture here.

02:45 So we have negative 1, negative 2, and negative 3 down here.

02:54 And finally i'm going to plot the points in red, so it makes them easier to see.

02:58 Now our first point 1, negative 1 3rd, well we see we have an x component of 1, so we move to the notch 1 here and we have a y component of negative 1 3rd so we move down from the origin about 1 3rd and so we want to find where these two points meet and it's about here and so i can't do that in this it follows that our point 1 negative 1 3rd lies here in the cartesian plane our next point, which is 0 .5 negative 1, well, 0 .5 is the same thing as a half.

04:01 So it's going to lie half between 0 and 1 on the x -axis.

04:05 And then we have y equals negative 1, which is this horizontal line here.

04:22 So we're finding where this vertical line and this horizontal meet, that is going to be our point...

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