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The mid points of the sides of the triangle ABC are D (6,1),E (3,5),and F(-1,-2) then the coordinates of the vertex opposite to D are?
M.P. of AB = DSo,coordinates of D (6,1)= (x1+x2/2,y 1+y2/2)=> x1+x2=12........eq(1)Co-ordinates of E(3,5)= (x2+x3/2,y2+y3/2)=> x2+x3=6.........eq(2)Co-ordinates of F(3,5)= (x3+x1/2,y3+y1/2)=> x3+x1=-2.........eq(3)eq(2)-(3) we get,x2-x1=8.........eq(4)eq(4)+(1) we get,x2=10,x1=2 and x3=-3Similarly find for y1,y2 and y3So,coordinates of D (6,1)= (x1+x2/2,y 1+y2/2)=> y1+y2=2........eq(5)Co-ordinates of E(3,5)= (x2+x3/2,y2+y3/2)=> y2+y3=10.........eq(6)Co-ordinates of F(3,5)= (x3+x1/2,y3+y1/2)=> y3+y1=-4........eq(7)eq(6)-(7) we get,y2-y1=14.........eq(8)eq(8)+(5) we get,y2=8,y1=-6 and y3=2So coordinates of A(2,-6) , B(10,8) and C(-3,2)Hence the vertex C(-3,2) is opposite to D
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