Question

the coordinates of A and B are 1,2 and 2,3 respectively. find the coordinates of r on line segment AB , so that AR/RB =4/3

Answer 1

Answer:

The coordinates of R is

$\displaystyle\bf(\frac{11}{7},\frac{18}{7})$

Step-by-step explanation:

$\textbf{Concept:}$

$\text{The co ordinates of the point which divides the line }$

$\text{segment joining (x_1,y_1) and (x_2,y_2) internally in the ratio m:n is}$

$\displaystyle(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$\textbf{Given:}$

$\frac{AR}{RB}=\frac{4}{3}$

$\implies\text{R divides AB internally in the ratio 4:3}$

$\text{Then, the coordinates of R is}$

$\displaystyle(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$\text{Here, (x_1,y_1)=(1,2) , (x_2,y_2)=(2,3) }$

$\displaystyle\implies(\frac{4(2)+3(1)}{4+3},\frac{4(3)+3(2)}{4+3})$

$\displaystyle\implies(\frac{11}{7},\frac{18}{7})$

$\therefore\text{Then the coordinates of R is }\displaystyle\bf(\frac{11}{7},\frac{18}{7})$

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.

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