Question

Properly design and label a coordinate system in the grid provided. Follow steps a – e. (7 points) a. Quadrants I – IV

b. x- and y- axes
c. a scale for the number lines (ex. going by 1’s, 2’s... write it in)
d. label the origin as point O
e. graph the coordinates A(-1, 2), B(3,0), and C(-4, -4).

Answer 1

To design a Cartesian coordinate system, draw intersecting perpendicular axes, label the quadrants, choose a uniform scale, mark the origin, and plot and label the given coordinates.

Step-by-step explanation:

To design and label a coordinate system on a grid, follow these steps:

1. Draw two perpendicular lines that intersect at the center of the grid. These are the axes. The horizontal axis is called the x-axis and the vertical axis is called the y-axis.
2. Label the quadrants formed by these axes as I (top right), II (top left), III (bottom left), and IV (bottom right).
3. Choose a scale for the axes, ensuring that it is uniform across the grid. Since there are no specific data points provided to suggest otherwise, we can label the axes with tick marks at every unit, i.e., 1, 2, 3, etc.
4. Label the point where the axes intersect as point O, which is the origin.
5. Plot the coordinates A(-1, 2) by moving 1 unit to the left of the origin and 2 units upwards. Plot B(3, 0) by moving 3 units to the right of the origin along the x-axis. Plot C(-4, -4) by moving 4 units to the left of the origin and 4 units down.

After plotting these points, make sure to label them accordingly on the graph. You have now completed a basic Cartesian coordinate system with labeled axes, scale, origin, and plotted points.