THEOREM 8-5Two nonvertical lines are perpendicular if, and only if, the slope of one is the negative reciprocal of the slope of the other line: .
To find the negative reciprocal of a number, first invert the number then change the sign. For example, to find the negative reciprocal of 4/3, you would first invert the number to get 3/4 and then change the sign (in this case from positive to negative) to get -3/4.
Two nonvertical lines are perpendicular if, and only if, the slope of one is the negative reciprocal of the slope of the other line:
can any one help me under stand this THEOREM
Not a tough as it looks
Let's suppose that the slope of some line = a/b
This theorem says that another line will be perpendicular if it has a negative reciprocal slope
The negative reciprocal of a/b = -b/a
Farther.....if we multiply these two slope together and the result = -1.....the lines are perpendicular
(a/b) (-b/a) =
- (a/b) (b/a) =
- (ab) / (ba) =
- (ab) / (ab) =
- 1 ,,,,so....we see that they are truly perpendicular lines !!!!!