Question

If the point c(-1.2) divides internally the line segment joining A(2, 5) and B in ratio 3 : 4.
find the coordinates of B.​

Answer 1

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Q1) If the point c(-1,2) divides internally the line segment joining A(2,5) and B in ratio 3:4 .Find The coordinates of B

$\: \: \bullet \underline{\bf{solution}}$

$\: \: \bullet\underline{ \boxed { \bf{by \: section \: formula}}}$

$\implies\displaystyle\tt{X=\dfrac{mx_1+nx_2}{m+n} \: and\: Y=\dfrac{my_1+ny_2}{m+n}}$

$\implies\displaystyle\tt{-1=\dfrac{3\times2+4\times x_2}{3+4}}$

$\implies\displaystyle\tt{-7=6+4x_2}$

$\implies\displaystyle\tt{-7-6-4x_2=0}$

$\implies\displaystyle\tt{-13-4x_2=0}$

$\implies\displaystyle\tt{x_2=\dfrac{-13}{4}}$

$\implies\displaystyle\tt{Y=\dfrac{my_1+ny_2}{m+n}}$

$\implies\displaystyle\tt{2=\dfrac{3\times5+4\times y_2}{7}}$

$\implies\displaystyle\tt{14=15+4y_2}$

$\implies\displaystyle\tt{14-15-4y_2}$

$\implies\displaystyle\tt{-1-4y_2=0}$

$\implies\displaystyle\tt{y_2=\dfrac{-1}{4}}$

$\bigstar\underline{\boxed{\bf \: B_coordinates=\: (x_2,y_2)=\bigg(\dfrac{-13}{4} ,\dfrac{-1}{4}\bigg) }}$