Question

Only for Brainly moderators , Brainly stars and brainly best users ▬▬▬▬ஜ۩۞۩ஜ▬▬Find the ratio in which point P whose ordinate is -3 divides the join of A(-2,3) and B(5,-15/2).​

Answer 1

$\large\underline{\sf{Solution-}}$

➢ Let the required ratio in which point P whose ordinate is -3 divides the join of A(-2,3) and B(5,-15/2). be k : 1.

↝  Let assume that the abscissa of Coordinate P be x, so that coordinate of P be (x, - 3).

We know,

Section Formula

Let us consider a line segment joining the points A (x₁ , y₁ ) and B (x₂ , y₂) and Let C (x, y) be any point on AB which divides AB internally in the ratio m : n, then coordinates of C is

$\red{\boxed{ \rm{ \:(x,y) = \bigg(\dfrac{mx_2 + nx_1}{m + n},\: \dfrac{my_2 + ny_1}{m + n} \bigg)}}}$

On substituting the values, we get

$\rm :\longmapsto\:(x, - 3) = \bigg(\dfrac{5k - 2}{k + 1}, \: \dfrac{ - \dfrac{15k}{2} + 3 }{k + 1} \bigg)$

On comparing, y - coordinates on both sides, we get

$\rm :\longmapsto\: - 3= \dfrac{ - \dfrac{15k}{2} + 3 }{k + 1}$

$\rm :\longmapsto\: - 3= \dfrac{\dfrac{ - 15k + 6}{2}}{k + 1}$

$\rm :\longmapsto\: - 3k - 3 = \dfrac{ - 15k + 6}{2}$

$\rm :\longmapsto\: - 6k - 6 = - 15k + 6$

$\rm :\longmapsto\: - 6k + 15k = 6 + 6$

$\rm :\longmapsto\:9k = 12$

$\rm :\longmapsto\:3k = 4$

$\bf\implies \:k = \dfrac{4}{3}$

• So, required ratio = 4 : 3

Additional Information :-

1. Distance Formula :

Let us consider a line segment joining the points A (x₁ , y₁ ) and B (x₂ , y₂), then distance between AB is

$\red{\boxed{ \: \: \: \rm{ \: AB = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } \: \: \: }}}$

2. Midpoint Formula :-

Let us consider a line segment joining the points A (x₁ , y₁ ) and B (x₂ , y₂) and Let C (x, y) be mid point on AB , then coordinates of C is

$\red{\boxed{ \: \: \: \rm{ \:(x,y) = \bigg(\dfrac{x_2 + x_1}{2},\: \dfrac{y_2 + y_1}{2} \bigg) \: \: \: \: }}}$