Like us!

Have a Look!

WhatsApp Message

Share Link

Mid Point Formula

Coordinate Geometry - Concepts

Distance Formula

Section Formula

Mid Point Formula

Trisection Points of Line

Area of Triangle Using Coordinate

Identification of Collinear Points

Cartesian Plane

Location of Coordinates in a Plane

Points lying on X-axis and Y-axis

Quadrants in the Cartesian Plane

Class - RRB Technician Grade I Signal Subjects

Concept Explanation

Mid-Point Formula

Coordinates of the mid-point M (x,y) of the segment AB are obtained by taking $m_1 = m_2$ in the section formula:

$x=frac{m_{2}x_{1}+m_{1}x_{2}}{m_{1}+m_{2}};and;y=frac{m_{2}y_{1}+m_{1}y_{2}}{m_{1}+m_{2}}$

$x=frac{m_{1}x_{1}+m_{1}x_{2}}{m_{1}+m_{1}};and;y=frac{m_{1}y_{1}+m_{1}y_{2}}{m_{1}+m_{1}}$

$x=frac{m_{1}(x_{1}+x_{2})}{2m_{1}};and;y=frac{m_{1}(y_{1}+y_{2})}{2m_{1}}$

$large x=frac{1}{2}(x_{1}+x_{2}),$ $large y=frac{1}{2}(y_{1}+y_{2}),$

Illustration: Find the distance of the point (1,2) from the mid-point of the line segment joining the points (6,8) and (2,4).

Solution: Let the points (1,2), (6,8), and (2,4) be denoted by A, B, and C respectively. Let M be the mid-point of BC. Coordinates of M, the mid-point of BC, are given by

$large left ( frac{6+2}{2},frac{8+4}{2} right )=(4,6)$

We have $large AM^{2}=(4-1)^{2}+(6-2)^{2}$

$large =3^{2}+4^{2}=9+16=25$

$large Rightarrow$ $large AM=sqrt{25}=5;units$

Illustration: Find the lengths of medians of the triangle with vertices A(2,2), B(0,2), and C(2,-4).

Solution: Let the coordinates of A, B, and C be (2, 2), (0,2), and (2, -4) respectively. Let D, E, F be the mid-points of BC, CA, and AB respectively.

Then the coordinates of D, E, F are given by

$large Dleft ( frac{0+2}{2},frac{2-4}{2} right )$ , $large large Eleft ( frac{2+2}{2},frac{2-4}{2} right )$ , $large Fleft ( frac{0+2}{2},frac{2+2}{2} right )$

or D (1, -1) E ( 2, -1) , F (1, 2)

$large therefore$ Length of median AD= $large sqrt{(1-2)^{2}+(-1-2)^{2}}=sqrt{10}$

Length of median BE= $large sqrt{(2-0)^{2}+(-1-2)^{2}}=sqrt{13}$

Length of median CF = $large sqrt{(1-2)^{2}+[2-(-4)]^{2}}=sqrt{37}$

$large therefore$ Lengths of medians are $large sqrt{10},sqrt{13},sqrt{37};;units$ .

Illustration: Three consecutive vertices of a parallelogram are A(1,2), B(1,0) C(4,0). Find the fourth vertex D.

Solution: Let coordinates of D be (x,y). As ABCD is a parallelogram, the diagonals AC and BD bisect each other. If M is the mid-point of AC, then coordinates of M are $large left ( frac{1+4}{2},frac{2+0}{2} right )=left ( frac{5}{2},1 right )$

As M is the mid-point of BD also, coordinates of M are $large left ( frac{1+x}{2},frac{0+y}{2} right )=left ( frac{1+x}{2},frac{y}{2} right ).$

We have $large left ( frac{1+x}{2},frac{y}{2} right )=left ( frac{5}{2},1 right ) Rightarrow frac{1+x}{2}= frac{5}{2};and;frac{y}{2}=1$

$large Rightarrow 1+x=5;and;y=2Rightarrow x=4,y=2$

$large therefore$ Coordinates of D are (4,2)

Coordinates of Centroid of Triangle

The centroid of a triangle is the point of concurrence of the medians of a triangle.

If G is the centroid of triangle ABC, then G divides the median AD in the ratio 2:1.

Let D be the mid-point of BC, the coordinates of D are $large left ( frac{x_{2}+x_{3}}{2},frac{y_{2}+y_{3}}{2} right ).$

As G(x,y) divides AD in the ratio 2 : 1

$large x=frac{1(x_{1})+2left ( frac{x_{2}+x_{3}}{2} right )}{2+1}=frac{x_{1}+x_{2}+x_{3}}{3}$

and $large y=frac{1(y_{1})+2left ( frac{y_{2}+y_{3}}{2} right )}{2+1}=frac{y_{1}+y_{2}+y_{3}}{3}$

Thus, the coordinates of the centroid are

$large left ( frac{x_{1}+x_{2}+x_{3}}{3},frac{y_{1}+y_{2}+y_{3}}{3} right )$

Illustration: Find the third vertex of the triangle whose two vertices are (-3,1) and (0,-2) and the centroid is the origin.

Solution: Let the two given vertices be A(-3,1) and B(0,-2). Let the third vertex be C(x,y) . Coordinates of the centroid of $large Delta ABC$ is given by

$large left ( frac{-3+0+x}{3},frac{1-2+y}{3} right )=left ( frac{-3+x}{3},frac{-1+y}{3} right )$ .

As the centroid of $large Delta ABC$ is given to be the origin,

we have $large left ( frac{-3+x}{3},frac{-1+y}{3} right )=(0,0)$

$large Rightarrow ;;-3+x=0,;;-1+y=0$

$large Rightarrow ;;x=3,;;y=1$

Thus, the coordinates of the third vertex are (3,1).

Sample Questions

(More Questions for each concept available in Login)

Question : 1

If the mid-point of the line segment joining the points A(3,4) and B(k,6) is P(x,y) and x+y-10=0,Find the value of k.
A. 7	B. -7	C. 5	D. 4
Right Option : A
View Explanation

Question : 2

The coordinates of the midpoint between points X(5, 3) and Y(7, 8).is _________________
A. $left ( 6,frac{11}{2} right )$	B. $left ( frac{2}{4},frac{11}{2} right )$	C. $left ( 6,2 right )$	D. None of these
Right Option : A
View Explanation

Question : 3

Using the midpoint formula, find the midpoint between points X(4, 3) and Y(3, 8).
A. $left ( frac{7}{2},11 right )$	B. $left ( 7,frac{11}{2} right )$	C. $left ( frac{7}{2},frac{11}{2} right )$	D. None of these
Right Option : C
View Explanation

Video Link - Have a look !!!

Language - English

Students / Parents Reviews [20]

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

Abhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of per...

Yogansh Nyasi

7th

Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from m...

Prisha Gupta

8th

We started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.

Manya

8th

Abhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.

Barkha Arora

10th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.

Eshan Arora

8th

When I have not joined Abhyas Academy, my skills of solving maths problems were not clear. But, after joining it, my skills have been developed and my concepts of science and SST are very well. I a...

Sharandeep Singh

7th

In terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...

Aman Kumar Shrivastava

10th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are v...

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...

Shreya Shrivastava

8th

My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.

Ayan Ghosh

8th

Third consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...

Ayan Ghosh

8th

Usually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...

Anika Saxena

8th

My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak poi...

Shivam Rana

7th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

Abhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary ...

Manish Kumar

10th

My experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should ...

Hridey Preet

9th

About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has...

Shreya Shrivastava

8th

View All

Attention !!!!!

Mid Point Formula

Mid-Point Formula

Coordinates of Centroid of Triangle

Students / Parents Reviews [20]

Aman Kumar Shrivastava

Yogansh Nyasi

Prisha Gupta

Manya

Barkha Arora

Yatharthi Sharma

Barkha Arora

Archit Segal

Eshan Arora

Sharandeep Singh

Aman Kumar Shrivastava

Shreya Shrivastava

Ayan Ghosh

Ayan Ghosh

Anika Saxena

Shivam Rana

Cheshta

Manish Kumar

Hridey Preet

Shreya Shrivastava