if and b are(-2,-2)and(2,-4)respectively. find the coordinate of p suc

1.	if and b are(-2,-2)and(2,-4)respectively. find the coordinate of p such that Ap=7/3AB and p lies on the line segment AB
Answer» Solution:- $\setlength{\unitlength}{<klux>2</klux>.5 cm}\begin{picture}(2,2)\thicklines\put(2,4){\line(2,0){<klux>3</klux>}}\put(3.5,4.1){\line(0,-1){0.2}}\put(1.8,3.8){\sf A(2,-2)}\put(3.5,3.7){\sf p}\put(4.8,3.8){\sf B (2,-4)}\put(2.7,4.1){\sf 3}\put(4,4.1){\sf 4}\end{picture}$ :- Given CO -ordinate is => A( - 2 , - 2 ) , B( 2 , - 4 ) :- Ratio are $\sf \to \:AP = \dfrac{3}{7} AB$ $\sf \to7AP = 3AB$ $\sf \to \:7AP = 3(AP + BP)$ $\sf \to \: 7AP = 3AP + 3BP$ $\sf \to \: 7AP - 3AP = 3BP$ $\sf \to \: 4AP = 3BP$ $\to \sf \: \dfrac{AP}{BP} = \dfrac{3}{4}$ :- Given ratio is 3 : 4 :- Formula $\sf \: x = \dfrac{mx_{2} + nx _{1}}{m + n} \: and \: \sf \: y= \dfrac{my_{2} + ny _{1}}{m + n} \:$ So $\sf \: \to \: m = 3 \: ,n \: = 4,x _{1} = - 2 ,x _{2} = - 2, y _{1} = 2, y _{2} = - 4$ $\sf \to \: x = \dfrac{3 \times - 2 + 4 \times - 2}{3 + 4} \: \: and \: \: y = \dfrac{3 \times 2 + 4 \times - 4}{3 + 4}$ $\sf\to \: x = \dfrac{ - 6 - 8}{7} \: \: and \: \: y = \dfrac{6 - 8}{7}$ $\sf \: \to \: x = \dfrac{ - 14}{7} \: and \: y = \dfrac{ - 2}{7}$

if and b are(-2,-2)and(2,-4)respectively. find the coordinate of p such that Ap=7/3AB and p lies on the line segment AB

Answer»

Solution:-

$\setlength{\unitlength}{<klux>2</klux>.5 cm}\begin{picture}(2,2)\thicklines\put(2,4){\line(2,0){<klux>3</klux>}}\put(3.5,4.1){\line(0,-1){0.2}}\put(1.8,3.8){\sf A(2,-2)}\put(3.5,3.7){\sf p}\put(4.8,3.8){\sf B (2,-4)}\put(2.7,4.1){\sf 3}\put(4,4.1){\sf 4}\end{picture}$