Maths / Coordinate Geometry / Section Formula

QUESTION

Determine the ratio in which the line 4x -3y +9 =0 divides the line segment joining the points (1, 3) and (2, 7).

EXPLANATION
Explain TypeExplanation Content
Text

Let the point divide the line in the ratio k:1

$\dpi{120} \fn_jvn \large x= \frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+ m_{2}}$

$\large \dpi{120} \fn_jvn \large x= \frac{kX2+ 1X 1}{k+ 1}= \frac{2k+1}{k+1}$

$\dpi{120} \fn_jvn \large y= \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+ m_{2}}$

$\dpi{120} \fn_jvn \large y= \frac{kX7+ 1X 3}{k+ 1}= \frac{7k+ 3}{k+1}$

putting these values in the equations 4x-3y +9 =0

$\dpi{120} \fn_jvn \large 4(\frac{2k+1}{k+1})- 3(\frac{7k+3}{k+1}) +9 =0$

$\dpi{120} \fn_jvn \large \frac{8k+4-21k-9 +9k+9}{k+1} =0$

$\dpi{120} \fn_jvn \large -4k +4 =0 \Rightarrow -4k = -4 \Rightarrow k=1$

so the line 4x-3y+9 divides the line segment joining the points (1,3) and (2,7) in the ratio 1:1

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