Question

Plot the points and draw line segments connecting the points to create the polygon. Then write a system of linear inequalities that defines the polygonal region. Rectangle: \((1,1),(7,1),(7,6),(1,6)\)

Short answer

The system of inequalities that defines the region enclosed by the rectangle is \(1 \leq x \leq 7\) and \(1 \leq y \leq 6\).

Step-by-step solution

Plot Points

Draw a Cartesian Plane. For each pair \((x,y)\) in the set \((1,1),(7,1),(7,6),(1,6)\), plot a point at the coordinates \((x,y)\). The x-coordinate represents the horizontal position and the y-coordinate represents the vertical position of each point.

Connect Points

Draw straight lines to connect the points in the following order: Connect \((1,1)\) to \((7,1)\), then \((7,1)\) to \((7,6)\), next from \((7,6)\) to \((1,6)\) and finally from \((1,6)\) to \((1,1)\). This forms a rectangle.

Establish Linear Inequalities

Based on the coordinates and the lines of the rectangle, we can derive these inequalities: For the horizontal sides, \(1 \leq y \leq 6\) and for the vertical sides, \(1 \leq x \leq 7\).