Question

Alan says that two lines in the coordinate plane are perpendicular if and only if the slopes of the lines are m and 1m. Identify and correct two errors in Alan’s statement.

Answer 1

Answer:

First, two lines are perpendicular if one has slope m, and the other has slope -1/m (Not 1m as Alan says)

That is the first error of Alan.

Now, there is another error.

If m = 0, then -1/m tends to minus infinity (in this case we would have a vertical line).

But we can not really divide by zero, so we should state that:

m can not be zero, if a line is horizontal, the perpendicular line must be vertical.