Question

9. The 'X' coordinate of the point which
divides the line segment joining the points
(4-3) and (8,5) in the ratio 3:1 is
O (a) 7
O (b) 3
O (c) 12
O (d) 4​

Answer 1

$\textbf{Given:}$

$\textsf{The line segment joining (4,-3) and (8,5) is divided internally}$

$\textsf{in the ratio 3:1}$

$\textbf{To find:}$

$\textsf{x co-ordinate of point of division}$

$\textbf{Solution:}$

$\textbf{Section formula:}$

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

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

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

$\textsf{Let P be the point of division}$

$\textsf{By section formula,}$

$\mathsf{The co-ordinates of P are given by}$

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

$\mathsf{=\left(\dfrac{3(8)+1(4)}{3+1},\dfrac{3(5)+1(-3)}{3+1}\right)}$

$\mathsf{=\left(\dfrac{24+4}{4},\dfrac{15-3}{4}\right)}$

$\mathsf{=\left(\dfrac{28}{4},\dfrac{12}{4}\right)}$

$\mathsf{=(7,3)}$

$\therefore\textsf{The x co-ordinate of P is 7}$

$\textbf{Answer:}$

$\textsf{option (a) is correct}$

$\textbf{Find more:}$

Find the co-ordinates of a point R when AR : RB = 2 :3 with A(1,3) and B(6,8).

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