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if a vortex of a triangle E(1,1) & the middle point of the sides through it (-2,3)&(5,2) find the other vorties

if a vortex of a triangle E(1,1) & the middle point of the sides through it (-2,3)&(5,2) find the other vorties

Grade:Upto college level

2 Answers

Rathod Shankar AskiitiansExpert-IITB
69 Points
10 years ago

Dear Satya Padhy,

 

the ratio middle points divides two vertex is 1:1

 

using formula      (x1*1 +x2*1)/(1+1) = -2       here   E(1,1)=(x1,y1)  and say A(x2,y2) B(x3,y3)

 

substitute x1 here   we get   x2=-4-x1 = -4-1 =-5

 

y2= 3-y1 = 3-1 =2

 

(x2,y2)=(-5,2)

 

x3= 5-x1= 5-1 =4

y3=2-1= 1

 

(x3,y3)=(4,1)

 

 


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Askiitians Expert

Rathod Shankar Singh

IIT Bombay

 

Anil Pannikar AskiitiansExpert-IITB
85 Points
10 years ago

Dear Satya,

 

 given middle point so it divides the line into 1:1

so,  -2 = (1 + x1)/2 or x1 = -5

and,  3 = (1 + y1)/2  or y1 = 5

so one of the vertex is (-5,5)

similarly find the other one.

 

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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Askiitians Expert

Anil Pannikar

IIT Bombay

 


 

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