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Content Area: Math
Index: 4.2C Grade 12 CPI 1
Standard: 4.2 - Geometry and Measurement
Strand: C - Coordinate Geometry
Cumulative Progress Indicator: 1 - The student will use coordinate geometry to represent and verify properties of lines · Distance between two points · Midpoint and slope of a line segment · Finding the intersection of two lines · Lines with the same slope are parallel · Lines that are perpendicular have slopes whose product is –1
Grade: 12
Sample Activities:
· Students construct a polygon that outlines the top view of their school. They are asked to imagine that they are architects who need to send this outline by computer to a builder who has no graphics imaging capabilities. They develop strategies for sending this information to the builder. One group locates one corner of the building at the origin and determines the coordinates for the other vertices. Another group uses vectors to tell the builder what direction to proceed from the initial corner located at the origin.
· Students work on the question of where a power transformer should be located on a line so that the length of the cable needed to run to two points not on that line is minimized. They find that if the two points are on the same side of the line, then by using reflections they can construct a straight line that crosses the given line at the desired location.
· Students first determine the coordinates for the vertices of a parallelogram, a rhombus, a rectangle, an isosceles trapezoid, and a square with one vertex at the origin and a side along the x-axis. They then work in groups to determine where the coordinate system should be placed to simplify the coordinate selection for a kite, a rhombus, and a square.
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