Question

If A (2, 2), B (−4, −4) and C (5, −8) are the vertices of a triangle, than the length of the median through vertex C is

Options

• \[\sqrt{65}\]

   

• \[\sqrt{117}\]

   

• \[\sqrt{85}\]

   

• \[\sqrt{113}\]

   

Answer 1

We have a triangle ΔABC  in which the co-ordinates of the vertices are A (2, 2) B (−4,−4) and C (5,−8).

In general to find the mid-point P (x , y)  of two points A(x₁ , y₁ ) and B (x₂ , y₂) we use section formula as,

`P(x , y) = ((x_1 + x_2 )/2 , (y_1 + y_2 ) / 2)`

Therefore mid-point D of side AB can be written as,

`D(x ,y ) = ((2-4)/2 , (2-4)/2)`

Now equate the individual terms to get,

x = -1 

y = - 1

So co-ordinates of D is (−1,−1)

So the length of median from C to the side AB,

`CD = sqrt((5 +1)^2 + (-8 + 2)^2)`

      `= sqrt(36 + 49 )`

      `= sqrt(85)`