How do you prove 2 perpendicular lines with gradient m1 and m2, have m1m2 = −1.?

Question

Prove the converse also. Thanks

This is impossible with yr 9 math

Answer 1

First of all, only use Yahoo Answers for some assistance if your textbook or your teacher is unclear.

Second, some students use Yahoo Answers to have other people do their homework and, in turn, they never learn much on their own.  Make sure this never happens to you.

Third, if two perpendicular lines have slopes m1 and m2 and if neither slope is equal to 0, then it is true that (m1)(m2) = -1.

Let me give an example that may assist you in writing your proof.  

1)  Draw a two-dimensional graph with an x-axis that is horizontal and a y-axis that is vertical.  

2)  Select two of the points (x, y) on the graph with different y values.  We'll use (0, 1) and (4, 2).

3)  Draw a straight line through the points for one of the two lines.  Call the line L1.

4)  The slope of L1 is equal to the change in the y values divided by the change in the x values when you go from (0, 1) to (4, 2).

m1 = (2 - 1) / (4 - 0) = 1 / 4.  

5)  Two lines are perpendicular if they form, at the point of intersection, four ninety degree angles (often called "right angles".)  For example, the x-axis and the y-axis are perpendicular.  

6)  If two lines are perpendicular and neither has a slope of 0, then one must have a positive slope and one must have a negative slope to form right angles.  

7)  To draw a line L2 that is perpendicular to L1 above beginning at (0, 1) , you can turn L2, ninety degrees counterclockwise by moving away from (0, 1) as before while replacing moving right with moving up, moving up with moving left, moving left with moving down and moving down with moving right.  

8)  The second point on L2 away from (0, 1) is where you will move up four units instead of right four units (adding 4 to the y value) and where you will move left insteal of up one unit (subtracting 1 from the x value).  The second point is

(0, 1) + (- 1, 4) = (- 1, 5)

9)  The slope of L2 is m2 = (5 - 1) / ( (-1) - 0) = 4 / (-1).

10)  Because you interchanged the numerator and denominator of m1 to reach m2 with their product being negative,

(m1)(m2) = - 1.

The converse is similar.