Question

The vertices of a triangle are A (3, -2) , B ( -2, 1) and C (5, 2) , Then the length of the median through B is

• A. $\sqrt{67}$ Units
• B. $\sqrt{37}$ Units
• C. $\sqrt{35}$ Units
• D. 6 Units

Answer 1

The correct option is B $\sqrt{37}$ Units

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 B will pass through the mid point of AC.
Using this formula, mid point of AC $=(\frac{3+5}{2},\frac{-2+2}{2})=(4,0)$
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 B$(-2,1)$ and D $(4,0)=\sqrt{{(4+2)}^2+{(0-1)}^2}=\sqrt{36+1}=\sqrt{37}$