Book Mark Book Mark delicious
Online Angle between two straight lines Tutor & Homework Help
Home > Online Tutoring > Co-ordinate Geometry > Angle between two straight lines
Tutors on NetTutors on Net
Solution Angle between two straight lines Parallel, Perpendicular Tutoring Online, Tutor Help
Angle between two straight lines Online Tutoring / Homework Help
ANGLES BETWEEN TWO STRAIGHT LINES:

THEOREM 1:

To find the angle between two given straight lines.

Solution:

Let the two straight lines be AT1 and AT2 which meet at x-axis at T1 and T2 points respectively.

Angle between two straight lines

Let the equations of the two lines AT1 and AT2 be

y = m1x + c1 and y2 = m2x + c2            (1)

Hence tan AT1X = m1 and tan AT2X = m2

Now ∠T1AT2 = ∠AT1X - ∠AT2X

Hence tan T1AT2 = tan [AT1X - AT2X]

Angle between two straight lines

Hence the required angle = ∠T1AT2

     Angle between two straight lines.       (2)

If equation (2) is a positive quantity then it is the tangent of the acute angle between the two lines, if (2) is a negative quantity then it is the tangent of the obtuse angle.

Example:

Find the angle between two straight lines y = 6x - 11 and Angle between two straight lines

Solution:

The equation of the first line is y = 6x - 11 which implies m1 = 6.

The equation of the second line is Angle between two straight lines hence


THEOREM 2:

To find the condition that two straight lines can be parallel.

Two straight lines are parallel when the angle between them is zero and hence the tangent of this angle is zero. Hence in theorem 1 the equation (2) becomes

       m1 = m2 which is the required result.

Example:

Find the equation of a straight line which passes through the point (4, -5) and which is parallel to the straight line 3x + 4y + 5 = 0.

Solution:

Any straight line which is parallel to 3x + 4y + 5 = 0 will be 3x + 4y + c2 = 0 because m1 = m2.

Now given that this line 3x + 4y + c2 = 0 passes through the point (4, -5) hence we get,

3. 4 + 4. (-5) + c2 = 0 or c2 = 8

Putting the value of c2 = 8 we get 3x + 4y + 8 = 0. (Answer)

THEOREM 3:

To find the condition that two straight lines can be perpendicular.

Let the two straight lines be y = m1x + c1 and y2 = m 2x + c2

If the angle between them is θ then by theorem 1,

          (1)

If the two lines are perpendicular then θ = 90 ο and so tan θ = ∞.

Hence in equation (1) which is only possible if the denominator is zero

Therefore the condition of perpendicularity is

1 + m1m2 = 0 or m1m2 = -1.

Hence the straight line y2= m2x + c2 is perpendicular to y = m1x + c1 if

Example:

Find the equation of a straight line which passes through the point (4, -5) and is perpendicular to the straight line 3x + 4y + 5 = 0.

Solution:

Let the equation of a straight line be y = m1x + c

Now given that this line passes through the point (4, -5) hence it becomes, -5 = 4m1 + c         (1)

Given that the above line is perpendicular to the straight line 3x + 4y + 5 = 0         (2)

From (2) we get where

Then by the condition of perpendicularity m1m2 = -1.

Hence

Or putting which in eq. (1) we get,

Hence the required equation will be Or 4x - 3y = 31         (Answer)


Online Solution Angle between two straight lines Help:

If you are stuck with a Solution Angle between two straight lines Homework problem and need help, we have excellent tutors who can provide you with Homework Help. Our tutors who provide Solution Angle between two straight lines help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Solution Angle between two straight lines Homework Help. Please do send us the Solution Angle between two straight lines problems on which you need Help and we will forward then to our tutors for review.


Online Tutor Angle between two straight lines Parallel, Perpendicular:

We have the best tutors in math in the industry. Our tutors can break down a complex Angle between two straight lines 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 Angle between two straight lines 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 Angle between two straight lines Parallel, Perpendicular tutoring and experience the quality yourself.