1. Understanding How to Plot a Point
Every point on the Cartesian plane is written as an ordered pair \((x, y)\). Plotting a point means marking its exact position based on these values.
To place the point correctly, we always move horizontally first (x-direction) and then vertically (y-direction).
1.1. Definition
Plotting a point means locating its position by moving x units left/right from the origin and then y units up/down.
2. Step-by-Step Method to Plot a Point
To plot a point \((x, y)\), follow these steps carefully:
2.1. Step 1: Start at the Origin
The origin is \((0,0)\). All movements begin from here.
2.2. Step 2: Move Along the x-axis
Look at the value of x:
- If x is positive → move right
- If x is negative → move left
2.3. Step 3: Move Parallel to the y-axis
After reaching the point on the x-axis, move vertically:
- If y is positive → move up
- If y is negative → move down
2.4. Step 4: Mark the Final Point
Where the horizontal and vertical movements meet, mark the point and label it.
2.4.1. Example
Plot \((4, -3)\):
- From origin, move 4 units right
- Then move 3 units down
- Mark the point in Quadrant IV
3. Understanding the Direction of Movement
Signs of the coordinates decide the direction in which we move:
3.1. Direction Rules
- +x → right
- -x → left
- +y → up
- -y → down
3.2. Quick Visual Summary
For \((x, y)\):
- Right & Up → Quadrant I
- Left & Up → Quadrant II
- Left & Down → Quadrant III
- Right & Down → Quadrant IV
4. Examples of Plotting Points
These examples help in understanding how the sign of each coordinate affects the final position.
4.1. Example 1
Plot \((2, 3)\):
- 2 units right
- 3 units up
- Point lies in Quadrant I
4.2. Example 2
Plot \((-4, 2)\):
- 4 units left
- 2 units up
- Point lies in Quadrant II
4.3. Example 3
Plot \((-3, -1)\):
- 3 units left
- 1 unit down
- Point lies in Quadrant III
4.4. Example 4
Plot \((5, -4)\):
- 5 units right
- 4 units down
- Point lies in Quadrant IV
4.5. Axis Examples
- \((0, 6)\) → on y-axis
- \((7, 0)\) → on x-axis