Problem Set for Previewing Unit 6
In the sixth unit of Math I students are shown coordinate geometry as the combination of geometry and algebra. We begin by introducing students to the coordinate plane and proving that the distance formula between two points is a product of the Pythagorean Theorem. Finally we show students the midpoint formula, for finding the midpoint of any two points. This unit is about learning to use the two formulas in the coordinate plane. We use these formulas then to prove or demonstrate that given figures have some of the properties that we taught in Unit 3.
Hand out to students a coordinate plane worksheet.
Have the students plot the points (0, 4) and (3, 0). If we wanted to create a right triangle using these two points where would the third point have to be?
What are the lengths of the legs of the triangle that can be created?
How can we find the length of the hypotenuse of this triangle? What is the length of the hypotenuse?
1) Repeat the investigation but this time use the points (2, 3) and (-1, -1). Where does the third point have to be in order to create a right triangle? How is this different than before?
2) What are the lengths of the legs of this right triangle?
3) What is the length of the hypotenuse of this right triangle?
4) Repeat this process using the points (x1, y1) and (x2, y2). What you find is the distance formula for any two points on the coordinate plane.
5) Using this formula find the distance for the following points:
a. (3, -2); (0, 9)
b. (-4, -4); (-2, 7)
c. (0, 0); (8, -5)
6) The midpoint of two points is found by finding the average of the x’s and the average of the y’s. Thus if we want to find the midpoint of (3, 2) and (5, 6) we have x = (3+5)/2 and y = (6+2)/2.