The product of the slopes of perpendicular lines equals -1
Solution:
Need to determine product of slope of perpendicular lines.
Product of slopes of perpendicular lines is always equal to -1.
lets verify this.
let consider following two equation of perpendicular lines
2x – y = 1
x + 2y = 2
Now evaluate slope of each line by representing them in slop intercept form that is y = mx + c
Where coefficient of x represents slope m.
Representing first line in slope intercept form we get
y = 2x – 1
On comparing above equation with slope intercept form we can say that its slope is 2.
Similarly representing x + 2y = 2 equation in slope intercept form we get
[tex]y=-\frac{1}{2} x+1[/tex]
On comparing above equation with slope intercept form we can say that its slope is [tex]\frac{-1}{2}[/tex]
On multiplying slopes of two perpendicular lines we get,
[tex]2 \times\left(-\frac{1}{2}\right)=-1[/tex]
Hence product of slope of perpendicular line is -1
