5. How is plotting \( (3,4) \) different from plotting \( (4,3) \) ?

To understand the difference between plotting the points \( (3,4) \) and \( (4,3) \), we need to consider the coordinates in the Cartesian coordinate system. 1. **Understanding Coordinates**: - A point in the Cartesian plane is represented as \( (x, y) \), where \( x \) is the horizontal coordinate (the position along the x-axis) and \( y \) is the vertical coordinate (the position along the y-axis). - The first number in the pair represents the x-coordinate, and the second number represents the y-coordinate. 2. **Plotting \( (3,4) \)**: - For the point \( (3,4) \): - Move 3 units to the right along the x-axis (since \( x = 3 \)). - Then move 4 units up along the y-axis (since \( y = 4 \)). - This point is located in the first quadrant of the Cartesian plane. 3. **Plotting \( (4,3) \)**: - For the point \( (4,3) \): - Move 4 units to the right along the x-axis (since \( x = 4 \)). - Then move 3 units up along the y-axis (since \( y = 3 \)). - This point is also located in the first quadrant of the Cartesian plane. 4. **Comparison**: - The two points \( (3,4) \) and \( (4,3) \) are different because they have different x and y coordinates. - Specifically, \( (3,4) \) is located at \( x = 3 \) and \( y = 4 \), while \( (4,3) \) is located at \( x = 4 \) and \( y = 3 \). - This means that \( (3,4) \) is to the left of \( (4,3) \) when plotted on the graph. In summary, the difference in plotting \( (3,4) \) and \( (4,3) \) lies in their positions on the Cartesian plane, which results from the order of their coordinates.