ABHYAS | Self Learning | Testing Platform

Course / Category - 10th NTSE

Like us!

Have a Look!

WhatsApp Message

Share Link

Class Syllabus

Study Notes

Practice Tests

Sample Papers

Video Lectures

Help - Video

Available Online Courses for selected Class / Category

NTSE

10th NTSE

BASIC

Free

Join Now Syllabus

Self Learning

Free Topics

(Click here to know About SELF LEARNING)

MOCK TESTS

Few Available

(Click here to attempt Free Mock Test)

Concepts Learning Progress

Available

Course Progess

Self Learning Progress

Report Card

Revision / Exam Preparation

Theory Notes

Question Bank

Subjects Related Concepts

Test Generator

Free Topics

Reports

Available as Required.

VIDEOS

Few Available

Join Now Syllabus

NTSE

10th NTSE

Self Learning

₹17200 ₹12000 +
Taxes

Join Now Syllabus

Self Learning

Available

(Click here to know About SELF LEARNING)

MOCK TESTS

(Click here to attempt Free Mock Test)

Concepts Learning Progress

Available

Test Generator

Syllabus / Topic Test

Solution and Detailed Analysis

Course Progess

Self Learning Progress

Report Card

Revision / Exam Preparation

Theory Notes

Test Generator

Subjects Related Concepts

Self Learning

Videos

Self Learning Exams

Practice

Self Learning - At Own Pace

Question Answers with Explaination

Reports

Question-wise Analysis

Strong, Moderate and weak Concepts

Remedial Tests for Weak Concepts

Achievements - Month/Subject & Subject / Month

Self Study Detail

Graphical View

Your Rankings - Month / Subject & Subject / Month

VIDEOS

799

SUBJECTS

Maths, Physics, Chemistry, Biology, English, History, Democratic Politics, Geography, Economics, Verbal Reasoning, Non Verbal Reasoning, Vedic Maths

Join Now Syllabus

(You can also select a particular Subject or Sub-Topic as per your choice to start with. Please sign-up and proceed. Selection of Subject and Sub-Topics will appear in Purchase section after Login. To sign-up, click here.)

Why ABHYAS?

Course Benefits

Interested in M&VP

Concept Detail

Maths / Coordinate Geometry / Area of Triangle Using Coordinate

(A Brief Glimpse of ABHYAS Content - Have aLook !!!!)

Area of Triangle Using Coordinate

We know that area of the trapezium ABCD whose two parallel sides are AB and DC and the distance between parallel sides is h, is given by

$large frac{1}{2}(AB+DC)h$

Let ABC be a triangle with vertices $large A(x_{1},y_{1}),B(x_{2},y_{2})$ and $large C(x_{3},y_{3})$ as shown in figure below.

Draw the ordinates AL, CM and BN.

Note that area of triangle ABC = Area of trapezium ALNB + Area of trapezium ACML - Area of trapezium BCMN

= $large frac{1}{2}(AL+BN)LN+frac{1}{2}(AL+CM)LM-frac{1}{2}(BN+CM)MN$

But $large AL=y_{1},BN=y_{2},CM=y_{3}$

$large LM=OM-OL=x_{3}-x_{1},MN=OM-ON=x_{3}-x_{2}$

$large and;LN=OL-ON=x_{1}-x_{2}$

$large therefore$ Area of triangle ABC

$large =frac{1}{2}(y_{1}+y_{2})(x_{1}-x_{2})+frac{1}{2}(y_{1}+y_{3})(x_{3}-x_{1})-frac{1}{2}(y_{2}+y_{3})(x_{3}-x_{2})$

$large =frac{1}{2}[(y_{1}+y_{2})x_{1}-(y_{1}+y_{2})x_{2}+(y_{1}+y_{3})x_{3}-(y_{1}+y_{3})x_{1}-(y_{2}+y_{3})x_{3}+(y_{2}+y_{3})x_{2}]$ $large =frac{1}{2}[(y_{1}+y_{2})x_{1}-(y_{1}+y_{3})x_{1}+(y_{2}+y_{3})x_{2}-(y_{1}+y_{2})x_{2}+(y_{1}+y_{3})x_{3}-(y_{2}+y_{3})x_{3}]$

$large =frac{1}{2}[x_1(y_{1}+y_{2}-y_{1}-y_{3})+x_2(y_{2}+y_{3}-y_{1}-y_{2})+x_3(y_{1}+y_{3}-y_{2}-y_{3})]$

$large =frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

How to obtain Area of a Triangle?

Rules to write down the area of a triangle whose vertices are given:

(i) Write down the coordinates of the vertices in order in two columns, repeating at the end the coordinates at the head,

(ii) draw diagonal arrows as in cross multiplication, and draw two vertical lines to enclose the two columns, and

(iii) prefix the factor $large frac{1}{2},$ thus getting

Simplification

Take the products of each row and the next crossway, putting the minus sign between them, as in cross multiplication, add the results, and multiply the sum by $large frac{1}{2}$ , thus getting

$large Delta =frac{1}{2}[x_{1}y_{2}-x_{2}y_{1}+x_{2}y_{3}-x_{3}y_{2}+x_{3}y_{1}-x_{1}y_{3}]$

Sign of Area: The areas of the triangles ABC and ACB are opposite in sign. In numerical cases, we usually ignore the sign of the area and take the absolute value of the area of the triangle as the final result.

Thus, we should write as follows:

$area; Delta ABC=frac{1}{2}left | x_{1}(y_{2}-y_3)+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}) right |$

That is, brackets in formula (1) have been replaced by the absolute value sign, $large parallel$ ,

Illustration: Find the area of the triangle whose vertices are (3,8),(7,2) and (-1,1).

Solution: The area of the triangle whose vertices are (3,8),(7,2),(-1,1) is

$large Delta= frac{1}{2}left | 6-56+7-(-2)-8-3 right |$

$large =frac{1}{2}left | 6-56+7+2-8-3 right |=frac{1}{2}left | -52 right |$

= 26 sq. units

A Brief Look

Course Progress PANEL

Student can view their progress from this panel.

Self Study

Student can learn from Self Study panel. Concept notes and Video will appear their to learn concept. Exam will be held on the basis of concepts learn.

Exam Evaluation PANEL

Detailed Exam Analysis for Offline and online exams will be Available in Student dashboard. Offline exams will be held for in-campus students only.

Class Notes PANEL

Student can view / download Class Notes assigned to them. Request can also be sent for elapsed Notes.

REPORT CARD

Report Card of each student is visble in Student Panel for WISE-FA, WISE-PT, WISE-Testing, Written Exams, Attendance, etc.

STUDENT PANEL

Ranking amongst the students of the class are visible at any time. Students rank will automatically based on the exams given by the students and score.

SELF LEARNING PANEL

Self Learning panel to know topics/concepts read and exams given. Detail analysis provided to students for exams given. Remedial papers will be generated on student choice for Weak Concepts.

TEST GENERATOR

Test generator to generate test for concepts taught and pending.

STUDENT DASHBOARD

To know Online and Offline exams given / pending with graphical view.

Why ABHYAS?

Course Benefits

Want Help?

Attention !!!!!

Available Online Courses for selected Class / Category

BASIC

Free

Self Learning

₹17200 ₹12000 + Taxes

Area of Triangle Using Coordinate

₹17200 ₹12000 +
Taxes