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 $\mathrm{C}$ - Noon Academy

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 $\mathrm{C}$

Maths | Previous Year Question Papers

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 $\mathrm{C}$

Coordinates of $\mathrm{A} \equiv(-1,3)$
Coordinates of $\mathrm{B} \equiv(1,-1)$
Coordinates of $\mathrm{C} \equiv(5,1)$
The median through the vertex $\mathrm{C}$ will meet at the mid point of $\mathrm{AB}$ . Coordinate of mid-point on $\mathrm{AB}=\left(\frac{(-1)+1}{2}, \frac{3+(-1)}{2}\right)=(0,1)$
Now,
Length of median through vertex $\mathrm{C}=$ Distance between $(5,1)$ and $(0,1)$
Therefore,
Length of median $=\sqrt{(0-5)^{2}+(1-1)^{2}}$
$\Rightarrow$ Length of median $=\sqrt{(5)^{2}}=5$ units
Hence the length of median through the vertx $\mathrm{C}$ is 5 units.

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