Question

The medians of a triangle meet at $(0,-3)$ and its two vertices are at $(-1,4)$ and $(5,2)$. Then the third vertex is

• A. $(4,15)$
• B. $(-4,-15)$
• C. $(-4,15)$
• D. $(4,-15)$

Answer 1

The correct option is B $(-4,-15)$

Given vertices $(-1,4)$ and $(5,2)$ the median meeta at centroid $(0,-3)$

we know that in a triangle with vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ then the centroid is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Let the third vertex be $(a,b)$

we have,

$(0,-3)=(\frac{-1+5+a}{3},\frac{4+2+b}{3})$

$0=\frac{-1+5+a}{3}\Rightarrow 0=\frac{4+a}{3}\Rightarrow 4+a=0\Rightarrow a=-4$

$-3=\frac{4+2+b}{3}\Rightarrow -3=\frac{6+b}{3}\Rightarrow -9=6+b\Rightarrow b=-15$

$\therefore (-4,-15)$ are the third vertex