Online Lengths of Perpendiculars Tutor & Homework Help
Solution Lengths of Perpendiculars Tutoring Online, Tutor Help
LENGTHS OF PERPENDICULARS:
THEOREM:
To find the length of the perpendicular let fall from a given point upon a given straight line.
1) Let the equation of the straight line be
x cos ∝ + y sin ∝ - p = 0
(1)
If p be the perpendicular on it, then
ON = p and ∠
XON = ∝.
Let the give point be P(x1, y1).
Draw a parallel PR to the given line to meet ON produced in R and draw PQ
(which is the required perpendicular).
If OR be p1, then the equation to PR will be,
x cos ∝ + y sin ∝ - p1 = 0
Since this passes through the point (x1, y1), we get
x1 cos ∝ + y1 sin ∝ - p1 = 0
or p1 = x1 cos ∝ + y1 sin ∝
But the required perpendicular = PQ = NR = OR - ON = p1 - p
= x1 cos ∝ + y1 sin ∝ - p (2)
Thus the length of the required perpendicular is obtained by substituting x1 and y1 for x and y
in the given equation.
2) If the equation of the straight line is
Ax + By + C = 0 (3)
Dividing the above equation by √(A2 )+ B2 we get,
Now comparing the above equation with eq. (1) we get,
Hence the perpendicular from the point (x1, y1) on equation (3) = x1 cos ∝+ y1 sin ∝ - p
Corollary:
The length of perpendicular from the origin i.e. from (0, 0) = 
Example:
Find the length of the perpendicular drawn from the point (4, 5) upon the straight line 3x + 4y = 10.
Solution:
We know that for the equation of straight line Ax + By + C = 0 the perpendicular from the point (x1, y1) on it =
Here (x1, y1) = (4, 5) and
the equation of the straight line is 3x + 4y = 10 or 3x + 4y - 10 = 0 so A = 3, B = 4 and C = -10
Online Solution Lengths of Perpendiculars Help:
If you are stuck with a Solution Lengths of Perpendiculars Homework problem and need help,
we have excellent tutors who can provide you with Homework Help. Our tutors who provide
Solution Lengths of Perpendiculars help are highly qualified. Our tutors have many years
of industry experience and have had years of experience providing Solution Lengths of
Perpendiculars Homework Help. Please do send us the Solution Lengths of Perpendiculars
problems on which you need Help and we will forward then to our tutors for review.
Online Tutor Lengths of Perpendiculars Parallel, Perpendicular:
We have the best tutors in math in the industry. Our tutors can break down a complex
Lengths of Perpendiculars Parallel, Perpendicular problem into its sub parts and explain
to you in detail how each step is performed. This approach of breaking down a problem has
been appreciated by majority of our students for learning Lengths of Perpendiculars Parallel,
Perpendicular concepts. You will get one-to-one personalized attention through our online
tutoring which will make learning fun and easy. Our tutors are highly qualified and hold
advanced degrees. Please do send us a request for Lengths of Perpendiculars Parallel,
Perpendicular tutoring and experience the quality yourself.
