# Equations of Parallel and Perpendicular Lines

The study of equations governing parallel and perpendicular lines is fundamental in the field of geometry and linear algebra. These mathematical expressions provide a concise representation of the relationships between lines in a two-dimensional plane. Understanding the distinct forms of equations for parallel and perpendicular lines is essential for solving various geometric problems and has practical applications in fields such as engineering, physics, and computer science. This topic serves as a cornerstone in developing a deeper comprehension of linear relationships and their geometric interpretations.

Questions

- A line passes through #(3 ,6 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- How are parallel and perpendicular lines used in real life?
- A line passes through #(5 ,8 )# and #(4 ,9 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- What is the slope-intercept form of the equation of the line through the point (-8, 7) and parallel to the line #x + y = 13#?
- A line passes through #(8 ,2 )# and #(6 ,7 )#. A second line passes through #(3 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(5 ,8 )# and #(2 ,9 )#. A second line passes through #(1 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(3 ,4 )# and #(7 ,3 )#. A second line passes through #(8 , 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(2 ,5 )# and #(0 ,1 )#. A second line passes through #(7 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(6 ,2 )# and #(6 ,7 )#. A second line passes through #(3 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(4 ,7 )# and #(2 ,8 )#. A second line passes through #(1 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(2 ,8 )# and #( 7, 2 )#. A second line passes through #( 6, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(5 ,0 )# and #(7 ,3 )#. A second line passes through #(3 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- The length of two adjacent sides of a parallelogram are in ratio 4:7and its perimeter is 132cm.find the lengths of all the sides of the parallelogram ?
- A line passes through #(8 ,5 )# and #(2 ,4 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- What is the equation of the tangent planes to #7x^2-3y^2-z^2+21=0# which passes through the line #7x-6y+9=0#,#z=3#?
- How do we find the equation of perpendicular bisector of a segment whose end points are #(-2,-1)# and #(-18,-5)#?
- A line passes through #(9 ,3 )# and #( 3, 5 )#. A second line passes through #( 7, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(9 ,2 )# and #( 3, 8 )#. A second line passes through #( 4, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(3 ,6 )# and #(4 ,8 )#. A second line passes through #(7 ,9 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- A line passes through #(2 ,3 )# and #( 4, 1 )#. A second line passes through #( 7, 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?