Choose 5 ordered pairs whose first component is the opposite of the second component. Plot these points and connect them. What kind of figure do you get? In what quadrants does the figure lie? Please help me - thanks!
a straight line through the origin that bisects the 2nd and 4th quadrants
Sketch it.
To find 5 ordered pairs where the first component is the opposite of the second component, we can follow these steps:
Step 1: Choose a value for the second component.
Step 2: Make the first component the opposite of the chosen value.
Step 3: Repeat steps 1 and 2 four more times, choosing different values for the second component each time.
Let's go through the steps:
Step 1: Choose a value for the second component. Let's choose -2.
Step 2: Make the first component the opposite of the chosen value. Therefore, the first component would be 2.
Step 3: Repeat steps 1 and 2 four more times, choosing different values for the second component each time.
- For the second pair, let's choose -4. The first component would be 4.
- For the third pair, let's choose -6. The first component would be 6.
- For the fourth pair, let's choose -8. The first component would be 8.
- For the fifth pair, let's choose -10. The first component would be 10.
So, the five ordered pairs are:
(2, -2)
(4, -4)
(6, -6)
(8, -8)
(10, -10)
Now, let's plot these points on a Cartesian plane:
| X (10,-10)
IV | X
|
-----|--------------------
III | X
|
|
-----|--------------------
| X
II |
|
|
-----|--------------------
I | X
|
|
|
|----------------------
I II III IV
Connecting the plotted points, we can see that the figure formed is a straight line passing through the origin (0, 0). The line goes from the second quadrant (II) through the origin to the fourth quadrant (IV).
To find five ordered pairs where the first component is the opposite of the second, you can select any number for the second component and make the first component its opposite. Here are five examples:
1. (-1, 1)
2. (-2, 2)
3. (-3, 3)
4. (-4, 4)
5. (-5, 5)
Now, let's plot these points on a coordinate plane:
| (5, -5)
---------------------
| (4, -4)
---------------------
| (3, -3)
---------------------
| (2, -2)
---------------------
| (1, -1)
---------------------
| (0, 0)
----------------------
| (-1, 1)
---------------------
| (-2, 2)
---------------------
| (-3, 3)
---------------------
| (-4, 4)
---------------------
| (-5, 5)
Now, when we connect these points, we get a straight line passing through the origin (0, 0). This line extends infinitely in both the positive and negative directions.
This figure is a straight line and it lies in quadrants I and III. Quadrant I is located above the x-axis and to the right of the y-axis, while quadrant III is below the x-axis and to the left of the y-axis.