Question

The point P(-4, 1) divides the line segment joining the points A(2, -2) and B in the ratio 3:5. Find the co-ordinates of point B.
plz give the correct answer ​

Answer 1

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

Given that

↝ The point P(-4, 1) divides the line segment joining the points A(2, -2) and B in the ratio 3:5.

↝ Let assume that coordinates of B be (x, y).

We know,

Section Formula,

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

So, on substituting the values, we get

$\rm :\longmapsto\:\:( - 4, 1) = \bigg(\dfrac{3x + 10}{3 + 5} , \dfrac{3y - 10}{3 + 5} \bigg )$

$\rm :\longmapsto\:\:( - 4, 1) = \bigg(\dfrac{3x + 10}{8} , \dfrac{3y - 10}{8} \bigg )$

$\rm :\longmapsto\:\dfrac{3x + 10}{8} = - 4 \: and \: \dfrac{3y - 10}{8} = 1$

$\rm :\longmapsto\:3x + 10 = - 32 \: \: and \: \: 3y - 10 = 8$

$\rm :\longmapsto\:3x= - 42 \: \: and \: \: 3y = 18$

$\rm :\longmapsto\:x= - 14 \: \: and \: \: y = 6$

Hence, Coordinates of B is ( - 14, 6 ).

Additional Information :-

1. Distance Formula

${\underline{\boxed{\rm{\quad Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \quad}}}}$

2. Midpoint Formula

${\underline{\boxed{\rm{\quad \dfrac{x_1 + x_2}{2} \; ,\; \dfrac{y_1 + y_2}{2} \quad}}}}$

3. Centroid of a triangle

${\underline{\boxed{\rm{\quad \bigg(\dfrac{x_1 + x_2 + x_3}{3} \; ,\; \dfrac{y_1 + y_2 + y_3}{3} \bigg)\quad}}}}$

4. Area of triangle

$\boxed{\rm\ Area =\dfrac{1}{2} [x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]}$

5. Conditions for 3 points to be collinear

$\boxed{\rm\ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) = 0}$