Question

The coordinate plane below represents a city. Points A through F are schools in the city.

graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.

Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)

Answer 1

The system of inequalities for points D and E in the overlapping shaded regions is −2≤x≤2 and 1≤y≤4. The corresponding lines will be vertical lines at x = -2 and x = 2, and horizontal lines at y = 1 and y = 4, forming a rectangular region shaded between these lines on the coordinate grid.

To create a system of inequalities that includes only points D and E in the overlapping shaded region, we need to consider the x and y coordinates of these points. Points D and E have x-coordinates within the range −2 ≤ x ≤ 2 and y-coordinates within the range 1≤y≤4.

The inequalities for the x-coordinates are −2≤x≤2, indicating that x must be between -2 and 2 (inclusive). The inequalities for the y-coordinates are 1≤y≤4, indicating that y must be between 1 and 4 (inclusive).

Graphically, these inequalities result in vertical lines at x = -2 and x = 2, and horizontal lines at y = 1 and y = 4. The shaded region is the rectangle formed by these lines, including points D and E.

The overlapping region represents the values of x and y that satisfy both sets of inequalities, ensuring that only points D and E are included in the shaded area.