Question

The point which divides the line segment joining the points $(3,4)$ and $(7,-6)$ internally into two parts such that one part is twice the other lies in which quadrant?

• A. I
• B. II
• C. III
• D. IV

Answer 1

The correct option is D IV

If a point divides the line segment $AB$ joining two points in given ratio $m:n$ internally, by section formula, the co-ordinates of a point are given as $=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

The ratio is $m:n=2:1$ and $A(x_1,y_1)$ = $(3,4)$ and $B(x_2,y_2)$ = $(7,-6)$

$\therefore$ Point $=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

$=(\frac{2\times 7+1\times 3}{2+1},\frac{2\times (-6)+1\times 4}{2+1})$

$=(\frac{17}{3},\frac{-8}{3})$

$\therefore$ The point lies in IV quadrant.