Question

If $A(2,2),B(-4,-4),C(5,-8)$ are the vertices of any triangle, then the length of median passing through $C$ will be:

• A. $\sqrt{65}$
• B. $\sqrt{117}$
• C. $\sqrt{85}$
• D. $\sqrt{113}$

Answer 1

The correct option is C $\sqrt{85}$

A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side.
Median passing through $C$ will pass through mid point of $AB$.
Mid point of two points ${(x}_1,y_1)$ and ${(x}_2,y_2)$ is calculated by the formula $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Using this formula, mid point of $AB=(\frac{2-4}{2},\frac{2-4}{2})=(-1,-1)$

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Distance between the points $C(5,-8)$ and $(-1,-1)=\sqrt{{(-1-5)}^2+{(-1+8)}^2}=\sqrt{36+49}=\sqrt{85}$