Question

If $A(-2,4)$, $B(0,0)$ and $C(4,2)$ are the vertices of a $\Delta ABC$, then find the length of median through the vertex A.

• A. 2
• B. 4
• C. 3
• D. 5

Answer 1

The correct option is D 5

A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side.
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 BC $D=(\frac{0+4}{2},\frac{0+2}{2})=(2,1)$

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Length of the median A$(-2,4)$ and D $(2,1)=\sqrt{{(2+2)}^2+{(1-4)}^2}=\sqrt{16+9}=\sqrt{25}=5$