M03 #15

If two lines have slopes \(m\) and \(n\) , respectively, are they perpendicular?

1. \(m*n=-1\)
2. \(m=-n\)

I have an issue in OE when explaining the statement 2. From OE shown below one can still answer the question that whether m & n are perpendicular.

I think in OE there should be two examples. First an example of two lines \(y= x+10\) & \(y=-x+10\), here you can see that the lines are parallel as the product of their slope is \(-1\). In second example we can quote \(y=10x\) & \(y=-10x\). Now its make more sense that statement 2 is insufficient.


OE:
Statement (2) by itself is insufficient. We only know that the lines have reciprocal slopes. For example line \(y=10x\) and \(y=-10x\) , are mirror reflections of each other on the x axis, but not perpendicular.