Find the length of the medians of the triangle whose vertices are (-1,3),(1,-1) and (5,1).
Answers
Answer:
Let the given points of a triangle be A(1, -1), B(0, 4), C(-5, 3).
Let D, E, F be the mid-points of the sides BC, CA and AB respectively. Then,
The co-ordinates of D are :
equals straight D open square brackets fraction numerator 0 plus 5 over denominator 2 end fraction comma space fraction numerator 4 plus 3 over denominator 2 end fraction close square brackets equals straight D open square brackets fraction numerator negative 5 over denominator 2 end fraction comma space 7 over 2 close square brackets
the co-ordinates of E are
equals straight E open square brackets fraction numerator negative 5 plus 1 over denominator 2 end fraction comma space fraction numerator 3 minus 1 over denominator 2 end fraction close square brackets equals space straight E space open square brackets fraction numerator negative 4 over denominator 2 end fraction comma space 2 over 2 close square brackets equals space straight E space left square bracket negative 2 comma space 1 right square bracket
the co-ordinates of F are
equals straight E space open square brackets fraction numerator 0 plus 1 over denominator 2 end fraction comma space fraction numerator 3 minus 1 over denominator 2 end fraction close square brackets equals straight E space open square brackets fraction numerator negative 4 over denominator 2 end fraction comma space 2 over 2 close square brackets equals straight E space left square bracket negative 2 comma space 1 right square bracket
the co-ordinates of F are
equals