Question

77.
Equation of the line dividing the joining the points (1, 1) and (2, 4) in the ratio 1 : 2 and
having slope 11 is
1)33x - 3y - 38 = ( 2) 33x - 3y - 38 = 0
3) 33x - 3y + 38=0 4) 33x + 3y +38=0​

Answer 1

$\textbf{Given:}$

$\textsf{Points are (1,1) and (2,4)}$

$\textbf{To find:}$

$\textsf{Equation of the line dividing the given points in the ratio 1:2}$

$\textsf{and having slope 11}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\textsf{The coordinates of the point which divides line joining (1,1) and (2,4)}$

$\textsf{internally in the ratio 1:2 is}$

$\mathsf{\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}$

$\mathsf{\left(\dfrac{1(2)+2(1)}{1+2},\dfrac{1(4)+2(1)}{1+2}\right)}$

$\mathsf{\left(\dfrac{4}{3},\dfrac{6}{3}\right)}$

$\mathsf{\left(\dfrac{4}{3},2\right)}$

$\textsf{Equation of the required line is}$

$\mathsf{y-y_1=m(x-x_1)}$

$\mathsf{y-2=11(x-\frac{4}{3})}$

$\mathsf{y-2=11\left(\frac{3x-4}{3}\right)}$

$\mathsf{3y-6=11(3x-4)}$

$\mathsf{3y-6=33x-44}$

$\textsf{Rearranging terms we get}$

$\mathsf{33x-3y-38=0}$

$\textbf{Answer:}$

$\mathsf{Option\;(2)\;is\;correct}$

$\textbf{Find more:}$

In what ratio is the line segment joining A(2,-3)&B(5,6) divided by x-axis also find the coordinate of the point of division.

https://brainly.in/question/7118881

Find the ratio in which the line segment joining the points (- 2 3) and (3 - 2) is divided by y axis​

https://brainly.in/question/14355682