Question 870004: the middle points of the sides of a triangle are ( 2,1)(-1,-3) and ( 4,5) respectively . find the coordinates of the vertices of the triangle
Answer by dkppathak(439)   (Show Source):
You can put this solution on YOUR website! the middle points of the sides of a triangle are ( 2,1)(-1,-3) and ( 4,5) respectively . find the coordinates of the vertices of the triangle
let vertex are A B C (x1,y1)(x2,y2)(x3,y3) respectively
using mid point formula mid pint of AB is (2,1)
2= X1+X2/2 than X1 +X2 =4 (1) and Y1 +Y2 = 2 (4)
similarly for BC AND AC
than X2 +X3 =-2 (2) and Y2 +Y3 = -6 (5)
X3 +X1 = 8 (3) and Y3 +Y1 = 10 (6)
by adding equation 1 2 and 3 for x and adding 4 5 6 for y
2X1+2X2 +2X3 = 10 and 2Y1 +2Y2 +2Y3 = 6
by taking 2 common for both equations
X1+X2 +X3 = 5 (7) and Y1 +Y2 +Y3 = 3 (8)
subtracting 1 2 3 from equation 7 and 4 5 6 from 8
X3=1 X1 = 3 X2 =-3 similarly Y3 = 1 Y1 =9 Y2 = -7
Answer vertex A =(3,9) B =(-3,-7) C =(1,1)
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