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Section and Mid-Point Formula — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsSection and Mid-Point Formula3 Marks
Question
The line segment joining the points $M(5, 7)$ and $N(-3, 2)$ is intersected by the y-axis at point $L.$ Write down the abscissa of $L.$ Hence, find the ratio in which $L$ divides $MN.$ Also, find the co-ordinates of $L.$
✓

Answer

Since, point $L$ lies on y-axis, its abscissa is $0.$
Let the co-ordinates of point $L$ be $(0, y).$ Let L divides MN in the ratio $k: 1.$ Using section formula, we have:
$x=\frac{k \times(-3)+1 \times 5}{k+1}$
$0=\frac{-3 k+5}{k+1}$
$-3 k+5=0$
$k=\frac{5}{3}$
Thus, the required ratio is 5 : 3.
Now, $y=\frac{k \times 2+1 \times 7}{k+1}$
$=\frac{\frac{5}{3} \times 2+7}{\frac{5}{3}+1}$
$=\frac{10+21}{5+3}$
$=\frac{31}{8}$

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