Question

The coordinates of which divides the line segment joining the points (3,-4) and (-2,5) in the ratio 1:3 is '

'(-7/4,-7/4)'

'(7/4,-7/4)'

'(-7/4,7/4)'

'(7/4,7/4)'​

Answer 1

Let , the coordinate point which divides the line segment joining the points A(3,-4) and B(-2,5) in the ratio 1:3 → be P ( x,y) .

Here,

• m : n → 1 : 3

$\bold{ \: \: \: \: \: \: x_1 = 3 \: \: \: \: \: \: \: \: , \: \: \: \: \: \: y_1 = -4 }$

$\bold{ \: \: \: \: \: \: x_2 = -2 \: \: \: \: \: \: \: , \: \: \: \: \: \: y_2 = 5 }$

Now,

$\color{blue} \bold{→ (x,y)= (\frac{m×x_2+ n×x_1}{m+n} , \frac{m×y_2+n×y_1}{m+n}</p><p>)}$

$\bold{→{(x,y) = ( \frac{1×( - 2)+ 3×3}{1 + 3} , \frac{1×5+3×( - 4)}{1 + 3}</p><p>})}$

$\bold{→{(x,y) = ( \frac{ - 2+ 9}{4} , \frac{5 - 12}{4}</p><p>})}$

$\boxed{ \color{red}\bold{→{(x,y) = ( \frac{ 7}{4} , \frac{ - 7}{4}</p><p>})}}$

So , the coordinate point P →

$\boxed {\underbrace{ \large \color{orange}{ \bold{( \frac{7}{4} \: \: \: ,</p><p> \frac{ - 7}{4} )}}}}$