Question

A (5, –1), B(–3, –2) and C(–1, 8) are the vertices of triangle ABC. Find the length of median through A and the coordinates of the centroid.

• A. √65 and (1/3,5/3)
• B. √55 and (1/3,5/3)
• C. √65 and (5/3,1/3)
• D. √61 and (5/3,1/3)

Answer 1

The correct option is A

√65 and (1/3,5/3)

Let AD be the median through the vertex A of $△ABC$. Then D is the mid-point of BC. So the coordinates are $(\frac{-3-1}{2},\frac{-2+8}{2})$ i.e., (-2, 3)

$\therefore AD=\sqrt{(5+2{)}^2+(-1-3{)}^2}$

= $\sqrt{49+16}=\sqrt{65}$ units

Let G be the centroid of $△$ ABC. Then G lies on median AD and divides it in ratio 2:1. The coordinates of G are

$(\frac{2\times (-2)+1\times 5}{3},\frac{2\times 3+\times (-1)}{2+1})$

= $(\frac{-4+5}{3},\frac{6-1}{3})$ = ($\frac{1}{3},\frac{5}{3}$)