Question

Find the co ordinates of the point which divides the line segment joining the points (6, 3) and (-4, 5) in the ratio 3 : 2 internally

• A. $(0,\frac{21}{5})$
• B. $(1,\frac{21}{5})$
• C. $(0,\frac{22}{5})$
• D. $(2,\frac{21}{5})$

Answer 1

Answer: (A)

$(0,\frac{21}{5})$

Let $P(x,y)$ be the point which divides the line segment $AB$ in the ratio 3:2 internally

$WeknowthatifapointP(x,y)dividesthelinesegmentABjoiningthepointsA(x_1,y_1)\&B(x_2,y_2)intheratiom:nthen,bythesectionformula,$

$\Rightarrow$ $P=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n_1}{m+n})$

$=(\frac{\left(3\right)(-4)+\left(2\right)\left(6\right)}{3+2},\frac{\left(3\right)\left(5\right)+\left(2\right)\left(3\right)}{3+2})$

$=(0,\frac{21}{5})$

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