Question

If A(-1, 3), B(1, -1) and C(5, 1) are the vertices of a triangle ABC find the length of the median passing through the vertex A.

• A. 5 units
• B. 6 units
• C. 15 units
• D. None of these

Answer 1

The correct option is A 5 units

A
median of a triangle is a line segment that joins the vertex of a triangle to
the midpoint of the opposite side.

Median through A passed through mid point of BC.
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 $=(\frac{1+5}{2},\frac{-1+1}{2})=(3,0)$

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 median through A $=\sqrt{{(3+1)}^2+{(0-3)}^2}=\sqrt{16+9}=\sqrt{25}=5units$