Find coordinates of a point which divides the line segment (6,-10) and

1.	Find coordinates of a point which divides the line segment (6,-10) and (3, -8) internally in a ratios 2:7
Answer» Topic :- Co-ordinate SYSTEM Given :- The point (6 , - 10) and (3 , -8 ) divides the line SEGMENT in RATIO 2 : 7 To find :- The co-ordinates of a point Solution:- If the point (x , y ) divides the line segment ${(x_1, y_1)}$ and ${(x_2,y_2)}$ in ratio m:n then ${(x,y)} = \bigg(\dfrac{mx_2+nx_1}{m+n} , \dfrac{my_2+ny_1}{m+n}\bigg)$ So, ${(x_1,y_1) = (6 , -10)}$ ${(x_2, y_2) =(3 , -8)}$ m : n = 2:7 Substuiting the values ${(x,y)} = \bigg(\dfrac{mx_2+nx_1}{m+n} , \dfrac{my_2+ny_1}{m+n}\bigg)$ ${(x,y)} = \bigg(\dfrac{2(3)+7(6)}{2+7} , \dfrac{2(-8)+7(-10)}{2+7}\bigg)$ ${(x,y)} = \bigg(\dfrac{6+42}{9} , \dfrac{-16-70}{9}\bigg)$ ${(x,y)} = \bigg(\dfrac{48}{9} , \dfrac{-86}{9}\bigg)$ So, the point (48/9, -86/9) divides the line segemnt (6,-10) and (3, -8) internally in a ratios 2:7 Know more :- Distance formula:- $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ Centroid formula:- $\bigg(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\bigg)$ Section formula External division $\bigg(\dfrac{mx_2-nx_1}{m-n}, \dfrac{my_2-ny_1}{m-n}\bigg)$ Mid point formula:- $\bigg(\dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2}\bigg)$