This is a multi-step analysis task. Students graph four linear functions. They find the intersections of those lines graphically and algebraically, determine the geometric shape (a rectangle) created by the intersections of the four lines, and find the area of it. To extend the analysis, students then create three equations of lines that form a triangle with the same area as the quadrilateral in the first part of the task.
Students need to know how to graph lines, how to prove intersections by solving systems of equations, use the distance formula to find the length of lines between points, and how to find the areas of a rectangle and a triangle.
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
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