Question

The medians of a triangle meet at $(1,1)$ and two of its vertices are $(2,5)$ and $(4,6)$.
Then the third vertex of the triangle is ..........

• A. $(-3,-8)$
• B. $(3,8)$
• C. $(0,-3)$
• D. $(3,5)$

Answer 1

Answer: (C)

$(0,-3)$

The equation for finding median of a triangle

$xM=\frac{xB+xC}{2}\text{and}yM=\frac{yB+yC}{2}$

Given the two vertices of triangle ,B(2,5) and C(4,6) and median of one side given as (1,1) .To find the vertices of A, consider the point B(2,5) and median (1,1) and vertices of A be $(x,y)$

$xM=\frac{xB+xA}{2}1=\frac{2+x}{2}\Rightarrow x=0yM=\frac{yB+yA}{2}\Rightarrow 1=\frac{5+y}{2}\Rightarrow y=-3$

$\therefore$ The vertices of $A(0,-3)$