## Section Formula

Section Formula:(Internally)

To find the coordinates of the point which divides internally the line segment joining two given points (x1,y1) and (x2,y2) in the given ratio m:n

Let A and B be the given two points (x1,y1) and (x2,y2)respectively.
Then the formula to find the point which is dividing the line-segment AB internally in the ratio m:n is given by

SectionFormula:(Externally)

To find the coordinates of the point which divides Externally the line segment joining two given points (x1,y1) and (x2,y2) in the given ratio m:n

Let A and B be the given two points (x1,y1) and (x2,y2)respectively.
The formula which is used to find the point which divides the line-segment AB externally in the ratio m:n is given by

Example 1

Find the point which divide the line segment joining the points (-1,2) and (4,-5) internally in the ratio 2:3.

Solution:

The above section-formula(internally) can be used to solve this problem.
Here, if we compare the the given points, ratio and formula, we get

(x1,y1) = (-1,2)

(x2,y2) = (4,-5)

m:n = 2:3

When we plug these information in the formula, we get the required point

Required point = [(2X4 +3x-1)/(2+3), (2X-5+3x2)/(2+3)]

= [(8-3)/5, (-10+6)/5]

= (1, -4/5)

Hence the required point is (1, -4/5)

Example 2

Find the point which divide the line segment joining the points (2,1) and (3,5) externally in the ratio 2:3.

Solution:

The above section-formula(externally) can be used to solve this problem.
Here, if we compare the the given points, ratio and formula, we get

(x1,y1) = (2,1)

(x2,y2) = (3,5)

m:n = 2:3

When we plug these information in the formula, we get the required point

Required point = [(2X3 -3x2)/(2-3), (2X5-3x1)/(2-3)]

= [(6-6)/-1, (10-3)/-1]

= (0, -7)

Hence the required point is (0, -7)

In the above two examples, it is very clear that how a point divides a line-segment internally and externally in the ratio m:n. For more examples and content in section-formula , you are requested to contact us through contact us page in our website.

Apart from the above two situations on section formula (dividing a line segment internally and externally in the given ratio m:n), we can do some other problems like, determining ratio when the point is given which is dividing  the line segment either internally or externally by using section formula. To get example  problems on section formula, kindly contact us.

We can do the other problems using the above formulas:

1. In what ratio, is the line segment joining the points A(4,4) and B(7,3) divided by the point C(-1,-1)?

2. Find the ratio in which the x-axis divides the line segment joining the points (1,2) and (-2,5)

3. Find the ratio in which the y-axis divides the line segment joining the points (3,0) and (-3,5).

4.Find in what ratio , the point p divides the line segment joining the two points A and B where A,B and P are respectively given by (11,7), (13,4) and (7,13).

Note for students:

When we work out problems in the topic Analytical Geometry, many students feel , it is very difficult to solve problems in the topic Analytical-Geometry. But, the real thing is not like that. Once we understand and remember the required formula, we can easily solve any kind of problems in the topic Analytical Geometry.

Important things to be followed, when problems are solved in the topic Analytical Geometry.

1. Problem should be read carefully.

2. Understanding of the problem is very important.

3. Take the inputs given in the problem.

4. Be clear with the out put expected in the problem.

5. Use appropriate formula.

6. Plug the given inputs in to the formula.

7. Get the required out put as result.

When students follow the above steps, they can easily any problem in the topic analytical geometry.

Related Topics

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