Answer :

Let the three coordinates of the larger triangle be (x1, y1), (x2, y2) and (x3, y3)


The three mid points on the three sides are (3, 3) , (4, 2) , (5, 4)


According to the section formula for mid points



x1 + x2 = 6 …Equation(i)



x2 + x3 = 8 …Equation (ii)



x3 + x1 = 10 …Equation(iii)


Solving Equation (i) ,(ii) and (iii)


x2 = 6 - x1


Putting this value in equation (ii) we get


x3 - x1 = 2 …Equation (iv)


Solving Equation (iii) & (iv)


2x3 = 12


x3 = 6


Putting in Equation (iv)


6 - x1 = 2


x1 = 4


Putting this value in equation (i)


4 + x2 = 6


x2 = 2



y1 + y2 = 6 …Equation (v)



y2 + y3 = 4 …Equation (vi)



y3 + y1 = 8 …Equation (vii)


Solving Equation (v) ,(vi) and (vii)


y2 = 6 - y1


Putting this value in equation (vi) we get


y3 - y1 = - 2 …Equation (viii)


Solving Equation (vii) & (viii)


2y3 = 6


y3 = 3


Putting in Equation (viii)


3 - y1 = - 2


y1 = 5


Putting this value in equation (v)


5 + y2 = 6


y2 = 1


The Vertices of the larger triangle are (4,5) , (2,1) , (6,3)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Cube and CuboidCube and CuboidCube and Cuboid41 mins
History - Concept and QuestionsHistory - Concept and QuestionsHistory - Concept and Questions57 mins
Resources and Development RevisionResources and Development RevisionResources and Development Revision28 mins
Heights and Distances-IHeights and Distances-IHeights and Distances-I45 mins
Sphere and HemisphereSphere and HemisphereSphere and Hemisphere16 mins
Right Circular Cone And FrustumRight Circular Cone And FrustumRight Circular Cone And Frustum43 mins
Corrosion: Types, Pros and ConsCorrosion: Types, Pros and ConsCorrosion: Types, Pros and Cons41 mins
Right Circular CylinderRight Circular CylinderRight Circular Cylinder45 mins
Revision on Substitution and  Elimination MethodRevision on Substitution and  Elimination MethodRevision on Substitution and Elimination Method44 mins
Economics - Concept and QuestionsEconomics - Concept and QuestionsEconomics - Concept and Questions59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

The coordinates oKerala Board Mathematics Part-2

The coordinates oKerala Board Mathematics Part-2

In this picture, Kerala Board Mathematics Part-2

What are the coorKerala Board Mathematics Part-2

Prove that if theKerala Board Mathematics Part-2

In the picture, tKerala Board Mathematics Part-2

The centre of cirKerala Board Mathematics Part-2

x1, x<Kerala Board Mathematics Part-2

A parallelogram iKerala Board Mathematics Part-2

The coordinates oKerala Board Mathematics Part-2