In the worksheet on plotting points in the coordinate plane, you are going to plot different types of co-ordinate points in the x-y plane. Well, look at the Plotting Points on a Coordinate Plane Worksheet below.
Plotting Points on a Coordinate Plane Worksheet
- Plot the points in the coordinate plane.
(i) (6, -2)
(ii) (-3, 7)
(iii) (2.5, 4.5)
(iv) (-5, -3.5)
- Please plotting the points in the same plane.
(i) (-2, -3)
(ii) (3, -2)
(iii) (5, 0)
(iv) (0, -1.5)
(v) (4.5, 1.5)
- Plotting the point in the x-y plane.
(i) (14, 5)
(ii) (25, -15)
(iii) (-0.8, 1.3)
(iv) (- , -1 )
- Plotting the points in the same figure.
(i) (5, -7)
(ii) (-6, 0)
(iii) (1, 5.5)
(iv) (-3, 8)
(v) (-3.5, -6.5)
- Plotting the points (15, -9) and (- 11, -19) in the same x-y plane.
Plotting Points on a Coordinate Plane
Here are some points to remember when plotting the given points in a coordinate plane:
- If the given point is in the form (+, +), then it is going to be located on the 1st quadrant
- If the given point is in the form (-, +), then it is going to be located on the 2nd quadrant
- If the given point is in the form (-, -), then it is going to be located on the 3rd quadrant
- If the given point is in the form (+, -), then it is going to be located on the 4th quadrant
- If the given point has the value 0 in x-coordinate, then it is going to be located on y-axis.
- If the given point has the value 0 in y-coordinate, then it is going to be located on x-axis.
How to Graph Points on the Coordinate Plane?
To graph points on the coordinate plane, you need to understand the organization of the coordinate plane and also know what to do with those (x, y) coordinates. If you want to know how to graph points on the coordinate plane, please follow these steps below.
Part 1: Understanding the Coordinate Plane
- Please understand the axes of the coordinate plane. When you are graphing a point on the coordinate plane, you are going to graph it in (x, y) form.
Here is what you will need to know:
- The x-axis will go left and right, the second coordinate is on the y-axis.
- The y-axis goes up and down.
- Positive numbers go up or right (based on the axis). Negative numbers will go left or down.
- Please understand the quadrants on the coordinate plane. You have to remember that a graph has 4 quadrants (usually labeled in Roman numerals). You need to know which quadrant the plane is in.
- Quadrant I will get (+,+), quadrant I is above and to the left of the y-axis.
- Quadrant IV will get (+,-), quadrant IV is below the x-axis and to the right of the y-axis. (5,4) is in quadrant I.
- (-5,4) is in Quadrant II. (-5,-4) is in Quadrant III. (5,-4) is in Quadrant IV.
Part 2: Graphing a Single Point
- Please start at (0, 0), or the origin. Then, go to (0, 0), which is the intersection of the x and y axes, right in the center of the coordinate plane.
- After that, move over x units to the right or left. Let us say that you are working with the set of coordinates (5, -4). Your x coordinate is 5. Since five is positive, you will need to move over five units to the right. If it was negative, you will move over 5 units to the left.
- Then, move over y units up or down. Please start where you left off. Because your y coordinate is -4, then you have to move down four units. If it were 4, you have to move up four units.
- In this step, you have to mark the point which you discovered by moving over 5 units to the right and 4 units down.
Part 3: Following Advanced Techniques
- You have to learn how to graph points if you are working with an equation. If you have a formula with no any coordinates, then you have to discover your points by choosing a coordinate for x and seeing what the formula spits out for y. Please keep going until you have discovered enough points and will be able to graph them all, connecting them if necessary.
- After that, connect the points if necessary. If you need to make a line graph, draw a circle, or connect all of the points of a parabola or another quadratic equation, then you have to connect the points. If you have a linear equation, then you are able to draw lines connecting the points from left to right. If you are working with a quadratic equation, then simply connect the points with curved lines.
- You have to understand how modifying the equation changes the graph.
Here are the different methods that modifying the equation changes the graph:
- Modifying the x coordinate will move the equation left or right.
- Adding a constant will move the equation up or down.
- Turning it negative (multiplying by -1) will flip it over; if it is a line, it is going to change it from going up to down or going down to up.
- Multiplying it by another number is going to increase or decrease the slope.
- Please follow an example to see how modifying the equation changes the graph. Then, consider the equation y = x^2, a parabola with its base at (0,0).
Here are the differences you are going to see when you modify the equation:
- y = (x-2)^2 is the same parabola, except it is graphed two spaces to the right of the origin; now its base is at (2,0).
- y = x^2 + 2 is the same parabola, except now it is graphed two spaces higher at (0,2).
- y = -x^2 is an upside down y = x^2; its base is (0,0).
- y = 5x^2 is a parabola, however it gets larger even faster, giving it a thinner look.