Points and Coordinates

The coordinates of a point give us directions so that we can locate it on a coordinate plane. In this lab you will learn to describe points in the plane and study the different parts of the coordinate plane.

Quadrants

Question 1. Look at the diagram shown below. The $x$-coordinate of the leftmost point is 1. What is the $y$-coordinate of this point?

Notice that your answer to the previous question is in the $y$ column of the first row of the table to the right. The same point is showing on the grid to the left. Fill in the $y$ value for the $x=2$ row of the table so that the points on the grid look like the diagram shown above.

$x$	$y$
1	2
2
3	2
4	2

Question 2. Click on to see the example for question 2. Complete this table so that the points on the grid to the left look like the diagram shown below.

$x$	$y$
	1
	2
2	3
2	4

Question 3. Click on to see the example for question 3. Complete this table so that the points on the grid look like the diagram shown below.

$x$	$y$
2	2
3	2
3
3
4

Question 4. Click on to see the example for question 4. Use the slider in the bottom left portion of your screen to change the value of $x_1$ for the point $(x_1,2)$. Click and drag the slider’s “handle” and notice how the point moves. Then use the left and right arrow keys to make small adjustments.

Does the point move horizontally or vertically as you change $x_1$?

Does the point move to the right or to the left as $x_1$ increases?

Slide $x_1$ to each value given here and complete the table.

$x_1$	$x$-coordinate	$y$-coordinate
2	2	2
4
-3

What is the relationship between $x_1$ and the $x$-coordinate of the point?

Question 5. Click on to see the example for question 5. Use the slider to change the value of $y_1$ and notice how the point $(2,y_1)$ moves.

Does the point move horizontally or vertically as you change $y_1$?

Does the point move up or down as $y_1$ increases?

Use the slider to complete this table.

$y_1$	$x$-coordinate	$y$-coordinate
2
4
-3

What is the relationship between $y_1$ and the $y$-coordinate of the point?

Question 6. Click on to see the example for question 6. Use the $x_1$ slider to change the $x$-coordinate of the point $(x_1,y_1)$. Use the $y_1$ slider to change the $y$-coordinate of the point. Notice how the point moves. The coordinates of the point are shown below the grid.

Use the sliders to find the coordinates of the origin.

( , )

Use the sliders to find the point $(2,0)$. Notice that this point is on the $x$-axis. Give the coordinates of two more points on the $x$-axis.

( , ) &
( , )

Use the sliders to find the point $(0,2)$. Notice that this point is on the $y$-axis (the vertical axis with the arrow at the top). Give the coordinates of two more points on the $y$-axis.

( , ) &
( , )

What axis do you think the point $(5,0)$ is on? Use the sliders to check your answer.

$(2,3)$ is in which quadrant? Use the sliders to check your answer. (Look back at the diagram at the beginning of this lab to refresh your memory about quadrants.)

$(-1,-3)$ is in which quadrant? Use the sliders to check your answer.

If a point has a positive $x$-coordinate and a negative $y$-coordinate, which quadrant is it in? Use the sliders to check your answer.

If a point has a negative $x$-coordinate and a positive $y$-coordinate, which quadrant is it in? Use the sliders to check your answer.

Question 7. Click on to see the example for question 7. Complete this table so that the points on the grid look like the diagram shown below.

$x$	$y$
2	2
1
	0
-1
-2

What do you notice about the $x$-coordinate and $y$-coordinate of each of the points?

Which of the following equations describes the relationship between the $x$- and $y$-coordinate of each point on the grid?
(i) $y=x$
(ii) $y=2x$
(iii) $y=x+2$

Your Name:
Your E-Mail Address:
Teacher's E-Mail Address: