Find the equation of a line that is perpendicular to a given line and passes through the point.
Straight lines are a very important topic one must understand in order to do well in coordinate geometry. They are used to graphically represent linear equations and fin their applications in various fields related to engineering and science. For understanding them, we first need to understand how an equation is represented by a straight line, and how to deal with perpendicular lines.
Answer: For a given straight line ax + by + c = 0, and given point (u, v), the equation of a line perpendicular to the given line and passing through the point is bx - ay + bu - av = 0.
Let's understand the explanation of the problem.
Let the given point be (u, v) and the given line be ax + by + c = 0.
Therefore, the family of such lines can be represented by,
bx - ay + þ = 0 ---- (1), where þ is a variable.
For a given point (u, v), we can find the value of þ, and hence find the straight line which passes through the given point as well.
Hence, we find the value of þ by substituting u and v in equation (1), that is, þ = bu - av.
Hence, For a given straight line ax + by + c = 0, and given point (u, v), the equation of a line perpendicular to the given line and passing through the point is bx - ay + bu - av = 0.