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

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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Rathod Shankar Singh

IIT Bombay

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.

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All the best.

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Askiitians Expert

Anil Pannikar

IIT Bombay