1.

Find the length of the median from the vertex B of ∆ABC whose vertices root 13 are A(1, -1), B(0, 4) and C(-5, 3)

Answer»

Find the length of the median from the vertex B of ∆ABC whose VERTICES  are A(1, -1), B(0, 4) and C(-5, 3) (correct question)

Given:

∆ABC whose vertices  are A(1, -1), B(0, 4) and C(-5, 3)

To find:

The length of the median from vertex B

Solution:

1) The median from vertex B will be the mid-point of AC.

2) COORDINATE of the foot of the median is given by:

Mid-point of AC

  • x = 1+(-5)/2 =-4/2 = -2
  • y = -1+3/2 = 2/2 = 1

Now, the vertex of the median is (0,4) and (-2,1)

3) We will find the length of the median by the distance formula,

\sqrt{(x2-x1)^{2}+(<klux>Y2</klux>-y1)^{2} }

(x1,y1) = (0,4)

(x2, y2) = (-2,1)

  • \sqrt{(-2-0)^{2}+(1-4)^{2} }
  • \sqrt{(-2)^{2}+(-3)^{2} }
  • \sqrt{4+9 }
  • \sqrt{13}

The length of the median is √13


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