Question

Find the coordinates of the point which divides the line segment joining (-1, 3) and (4, -7) internally in the ratio 3:4.

Answer 1

Answer:

the coordinates of the point which divides the line segments joining the points (1,-2,3)and (3,4,-5) in the ratio 2:3 (1) internally ,and (2) externally

Answer 2

Answer:

${ \large{ \pmb{ \sf{★Given... }}}}$

Points: A(-1, 3) , B(4, -7)

Ratio : 3 : 4

${ \large { \pmb{ \sf{★ To \: Find... }}}}$

Coordinates of the points..?

${ \large{ \pmb{ \sf{★ Formula \: Used... }}}}$

${ \sf{p(x, y) = \bigg( \frac{m x_{2} + n x_{1}}{m + n} , \frac{my_{2} + ny_{1}}{m + n} \bigg) }}$

${ \large{ \pmb { \sf{★ Solution... }}}}$

From points,

• ${ \sf{ x_{1} = - 1}}$
• $\: { \sf{ x_{2} = 4}}$
• $\: { \sf{ y_{1} = 3}}$
• $\: { \sf{ y_{2} = - 7}}$

And, m : n = 3 : 4

Substitute these values in formula,

$\implies{ \sf{ \bigg( \frac{3 (4) + 4 ( - 1)}{3 + 4} , \frac{3( - 7) + 4(3)}{3 + 4} \bigg) }}$

$\: \implies{ \sf{ \bigg( \frac{12 - 4}{7} , \frac{ - 21 +12}{7} \bigg) }}$

$\implies{ \sf{ \bigg( \frac{8}{7} , \frac{ - 9}{7} \bigg) }}$

${ \large{ \pmb{ \sf{★ Final \: Answer... }}}}$

$\therefore{ \bf{ p(x, y) = \bigg( \frac{8}{7} , \frac{ - 9}{7} \bigg) }}$