Question

The point (11, 10) divides the line segment joining the points (5, -2) and (9, 6) in the ratio

• A. 1 : 3 internally
• B. 1 : 3 externally
• C. 3 : 1 internally
• D. 3 : 1 externally

Answer 1

The correct option is D 3 : 1 externally

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Let the ratio be $k:1$

Substituting $(x_1,y_1)=(5,-2)$ and $(x_2,y_2)=(9,6)$ in the
section formula, we get $(\frac{k\left(9\right)+1\left(5\right)}{k+1},\frac{k\left(6\right)+1(-2)}{k+1})=(11,10)$

$(\frac{9k+5}{k+1},\frac{6k-2}{k+1})=(11,10)$

Comparing the x - coordinate,
$=>\frac{9k+5}{k+1}=11$

$=>9k+5=11k+11$

$2k=-6$

$k=-3$

Hence, the ratio is $3:1$ externally.