Question

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

• A. $5units$
• B. $3units$
• C. $8units$
• D. $7units$

Answer 1

The correct option is A $5units$

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 $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
The median through A will pass through mid point of BC which is say D.
Using this formula, mid point of BC $= \left( \frac { 1 + 5 }{ 2 } ,\frac { - 1 + 1 }{ 2 \right) \quad =\quad (3,0) $

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Distance between the points A$(-1,3)$ and D $(3,0)=\sqrt{{(-1-3)}^2+{(3-0)}^2}=\sqrt{16+9}=\sqrt{25}=5$