Perpendicular Lines

 To investigate the relationship between perpendicular lines I first needed to construct some. This was very similar to the parallel lines. First I plotted two points and using the line tool constructed a line through the two points. Then I plotted a third point not on the line. Next I used the perpendicular line tool and constructed a line through the third point that is perpendicular to the line. For a line to be perpendicular to another line, they must intersect at a right angle. Then I found the slope using the slope tool and found the equations of each line from the algebra section. I repeated this three times so I would have three different sets of perpendicular lines.  I looked at the three different sets of lines and observed that one was decreasing and one way increasing. I saw this from just looking at the lines, not their slopes. This observation was confirmed with their slope values. For example line A has a positive slope of 2 and line B has a negative slope of -0.5. I saw this to be true for lines C and D and also lines E and F. To better see the different slopes here is a table. Looking at lines E and F we see that the only difference is that E is positive 1 and F is negative 1. There is not change in numeric slope. However for A and B and C and D we notice a change other than the positive and negative. To better see the relationships between the slopes, lets convert the decimals to fractions. We know that  and  therefore we can say that  and . From this we can see that these slopes are the "flipped" values of the opposite lines slopes. For example slope of  and . We can call this the reciprocal. We know from previous knowledge that  and so . For the case of the lines with a slope of 1, this does not change because the reciprocal of 1 is 1. Therefore we can make the conjecture that for two lines to be perpendicular their slopes must be the negative reciprocal of each other. Generalized we can say the slopes of perpendicular lines should be m and