Question

Find the co-ordinates of a point R when AR : RB = 2 :3 with

A(1,3) and B(6,8).​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{AR:RB=2:3 with A(1,3) and B(6,8)}$

$\underline{\textsf{To find:}}$

$\textsf{The co-ordinates of R}$

$\underline{\textsf{Solution:}}$

$\textbf{Section formula:}$

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

$\mathsf{line\;segment\;joining\;(x_1,y_1)\;and\;(x_2,y_2)\;internally\;in\;the\;ratio \;m:n\;are}$

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

$\mathsf{Consider, AR:RB=2:3}$

$\implies\textsf{R divides the line segment AB internally in the ratio 2:3}$

$\textsf{Using Section formula,}$

$\textsf{The co-ordinates of R is given by}$

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

$\mathsf{(\dfrac{2(6)+3(1)}{2+3},\dfrac{2(8)+3(3)}{2+3})}$

$\mathsf{(\dfrac{12+3}{5},\dfrac{16+9}{5})}$

$\mathsf{(\dfrac{15}{5},\dfrac{25}{5})}$

$\mathsf{(3,5)}$

$\underline{\textsf{Answer:}}$

$\textsf{The co-ordinates of R is (3,5)}$

Find more:

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Answer 2

Answer:

your answer is

a. 3

b. 6

Step-by-step explanation:

hope that helps