If the two lines are perpendicular then the two vectors AB and CD are orthogonal and their scalar product must be zero. Hence
> 1 , m1> . > 1 , m2> = 0
1 + m1 * m2 = 0
The above may be written as
m1 * m2 = - 1
m1 = - 1 / m2 , m1 is equal to the negative reciprocal of m2
m2 = - 1 / m1 , m2 is equal to the negative reciprocal of m1
NOTE: Points A, B, C and D and their x coordinates can choosen anywhere on the two lines. As an exercise choose other values for the x coordinates of points A, B, C and D and redo the calculation above. You should be able to make the same conclusion concerning the slopes of two perpendicular lines.