Question

The line $x+y=4$ divides the line joining the points $(-1,1)$ and $(5,7)$ in the ratio.

• A. $3:1$
• B. $1:2$
• C. $1:2$ externally
• D. None of these

Answer 1

The correct option is A $3:1$

$\begin{array}{c}x+y=4\to \left(i\right)\\ \left(-1,1\right)\overline{}\left(5,7\right)\\ Thee{q}^{n}oflinejoiningtwopointsis\\ \frac{y-1}{x+1}=\frac{6}{6}\left[\begin{array}{c}\because weknowfromslopeformula\\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_2}\end{array}\right]\\ \frac{y-1}{x+1}=1\\ y-1=x+1\\ y-x=2\\ x-y=-2\to \left(ii\right)\\ Solving60the{q}^{n}weget.\left(x\right)\\ x+y=4\\ \underset{–}{x-y=2}\\ 2x=6\\ x=3\\ andfrome{q}^n\to \left(ii\right)\\ x=y-2\\ x+2=y\\ 5=y\\ Letlinedividethejoiningtwopointsin\lambda :1ratio\\ Then,\end{array}$