Question

The vertices of a triangle are A(-1,3), B(1,-1) and C(5,1). Find the length of the median through the vertex C

Answer 1

In a triangle of ABC. Let the midpoint be D which lies in between B and C

So, D = (1+5/2, -1+1/2) = (3,0)

So, Length of median = root of (-1-3)^2  + (3-0)^2

                                    = root of (4)^2 + (3)^2

                                   = root 16 + 9

                                   = root 25

                                   = 5


Hope this helps!

Answer 2

Answer:

The length of the median through the vertex $C$ is $5$ units.

Step-by-step explanation:

Given :    Coordinates of  $A=(-1,3)$   $=(x_{1} , y{1} )$

               Coordinates of $B=(1,-1)$    $=(x_{2} , y{2} )$

                Coordinates of $C=(5,1)$     $=(x_{3} , y{3} )$

To Find :  The length of the median through the vertex C

We know that the median through the vertex $C$ will meet the side $AB$ at its mid-point.

Let the mid-point on side AB be the point $D$ with coordinates $(x,y)$ .

$\implies D= (x,y)=\frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2}$

                $=\frac{(-1)+1}{2} , \frac{3+(-1)}{2}$

                $=(0,1)$

Now,

Length of median through point C  = Distance between vertex $C$ and  $D$                        

                                                           = Distance between $(5,1)$and  $(0,1)$

Therefore,

Length of median = $\sqrt{(0-5)^{2} + (1-1)^{2} }$

                             $=\sqrt{5^{2} }$

                             $=5$ units

Hence, the length of the median through the vertex $C$ is $5$ units.

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