Answer :
Answer:
a. They have negative reciprocal slopes.
Step-by-step explanation:
When two lines are perpendicular then slopes of two perpendicular lines are opposite reciprocal.
For example, we take two lines one line passing through the points A(2}{,1) and B(3,2) and another line passing through the points C(1,-1) and D(2,-3)
The slope of line AB ,[tex]m_1=\frac{2-1}{3-1}=\frac{1}{2}[/tex]
Using slope formula :
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of line CD,[tex]m_2=\frac{-3+1}{2-1}[/tex]
Slope of line [tex],m_2=-2[/tex]
Slope of line AB,[tex]m_1=-\frac{1}{m_2}[/tex]
Slope of line AB,[tex]m_1=-\frac{1}{-2}=\frac{1}{2}[/tex]
Hence, Slopes of two lines AB and CD are opposite reciprocals. Therefore,the lines AB and CD are perpendicular.
Answer :a. They have negative reciprocal slopes.