Question

How Do I Solve Question 8 ?

Answer 1

8)

$\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(x,y)\qquad C(12,5)\qquad \qquad AB:BC\qquad 3:4\to \frac{3}{4} \\\\\\ \cfrac{AB}{BC} = \cfrac{3}{4}\implies \cfrac{A}{C}=\cfrac{3}{4}\implies 4A=3C\implies 4(x,y)=3(12,5) \\\\\\ -------------------------------\\\\ { B=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}\\\\ -------------------------------$

$\bf B=\left(\cfrac{(4\cdot x)+(3\cdot 12)}{3+4}\quad ,\quad \cfrac{(4\cdot y)+(3\cdot 5)}{3+4}\right)=\stackrel{B}{(4,1)} \\\\\\ \left(\cfrac{4x+36}{7}~,~\cfrac{4y+15}{7} \right)=(4,1)\implies \begin{cases} \cfrac{4x+36}{7}=4\\\\ 4x+36=28\\ 4x=-8\\ \boxed{x=-2}\\ ----------\\ \cfrac{4y+15}{7}=1\\\\ 4y+15=7\\ 4y=-8\\ \boxed{y=-2} \end{cases}$