Question

The coordinates of the point(s) which divide(s) the line segment joining the point $(5,-2)$ and $(9,6)$ in the ratio $3:1,$ are

• A. $(11,10)$
• B. $(8,4)$
• C. $(10,11)$
• D. $(4,8)$

Answer 1

Answer: (A), (B)

The correct options are
A $(11,10)$
B $(8,4)$

Let $A\equiv (5,-2)$ and $B\equiv (9,6).$
Let $P(x,y)$ divides $AB$ in the ratio $3:1.$

When division is internal,
$P\equiv (\frac{3\left(9\right)+1\left(5\right)}{3+1},\frac{3\left(6\right)+1(-2)}{3+1})P\equiv (8,4)$

When division is external,
$P\equiv (\frac{3\left(9\right)-1\left(5\right)}{3-1},\frac{3\left(6\right)-1(-2)}{3-1})P\equiv (11,10)$