Activity 3
 Exploration 2

In this exploration, you use technology to model the process described in 
Exploration 1.  Most geometry utilities have reflection tools for finding the images of objects.  To use this feature, you must first define a mirror line and the points to be reflected.

a.	1.	Construct a mirror line segment, AB.

	2.	Construct two points, P and Q, on the same side of AB. 

3.	Reflect points P and Q in AB and label the images P' and Q', respectively. 

4.	Construct PQ' and QP'. 

5.	Construct a point C at the intersection of AB and PQ'.

6.	Measure <PCA and <QCB.	<PCA = _____	<PCA = _____
Label these angles on the diagram with these measurements.

7.	Construct PP' and QQ'.

8.	Construct a point at the intersection of AB and PP' and label it as point D.  Construct a point at the intersection of AB and QQ' and label it as point E.  Your construction should now resemble this figure.

9.	Measure <PDA and <QEB.  <PDA = _____ and <QEB = _____
Label these angles on the diagram with these measurements.

10. 	Measure the distances from AB to points P, P', Q, and Q'.
	The distance from AB (at D) to P is _____units.
	The distance from AB (at D) to P' is _____units.
	The distance from AB (at E) to Q is _____units.
	The distance from AB (at E) to Q' is _____units.
Label these distances on the diagram with these measurements.

b. 	Use your measurements in Part a to make a conjecture about the 
relationship between AB and QQ':
 _______________________________________________________
_______________________________________________________
	_______________________________________________________

c. 	Select and move various points on your construction.  Note any relationships you observe among the measurements of angles and segments as you move the points.

d.	Complete Steps 1-3 below using your construction from Part a. 

1.	Construct a point S anywhere on AB. 

2.	Construct line segments QS and SP.  Measure QS on your calculator.  Measure SP on your calculator.  Add the two measurements on your calculator to measure the total distance traveled when moving from Q to S and then from S to P.

3.	By moving S along AB, find the point where the total distance traveled in Step 2 is shortest.