Question

The coordinate plane below represents a community. Points A through F are houses in the community.

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 B and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)

Part B: Explain how to verify that the points B and F are solutions to the system of inequalities created in Part A. (3 points)

Part C: John wants to live in the area defined by y > 2x − 5. Explain how you can identify the houses in which John is interested in living. (2 points)


HELPPPPP!!!!!!

Answer 1

Part A: Points B and F are one edge of the convex quadrilateral that contains all of the points, so only one inequality is necessary. In the figure, we have chosen to graph
2x + 7y < 0
It is shown as a blue dashed line through the origin with shading below the line. It has a slope of -2/7, which makes it parallel to the line through points B and F.

If you want two inequalities, you could use
y < 0
x < 4
These will graph as dashed horizontal and vertical lines, with shading below and to the left. The doubly-shaded area will include points B and F.

Part B: One can verify that points B and F are solutions to the system of inequalities either by putting their coordinates into the inequalities, or by consulting the graph.

Part C: You can identify the houses of interest to John by graphing the inequality and identifying the points that are in the solution space. In the attached graph, that inequality is graphed in pink. The houses of interest to John are shown to be B, D, D, E. Houses A and F are not in the solution space.