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.

__Vocabulary__

Distance Midpoint Coordinate
Plane Pythagorean
Theorem

__Investigation__

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?

__Additional Questions__

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
(x_{1}, y_{1}) and (x_{2}, y_{2}). 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.

More practice can be found using Kuta Software’s
free worksheets. Midpoint Distance