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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry3 Marks
Question
Find the ratio in which the $y-$axis divides the line segment joining the points $(-4,-6)$ and $(10,12)$ Also find the coordinates of the point of division.
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Answer

Let us assume a point such that that the line joining the points $(-4,-6)$ and $(10,12)$ in the ratio $k: 1$
Let this point on the $y$ axis be $(0, y)$
Now using the section formula
$P=\left(\frac{m x_2+n x_1}{m+n}, \frac{m y_2+n y_1}{m+n}\right)$
$(0, y)=\left(\frac{10 k-4}{k+1}, \frac{12 k+(-6)}{k+1}\right)$
On comparing the $x$ coordinate of both the sides.
$\Rightarrow \frac{10 k+(-4)}{k+1}=0$
$\Rightarrow 10 k-4=0$
$\Rightarrow k=\frac{4}{10}=\frac{2}{5}$
and, $y=\frac{12 k-6}{k+1}$
Substituting the value of $k$,
$y=\frac{12 \times \frac{2}{5}-6}{\frac{2}{5}+1}$
$\Rightarrow y=-\frac{6}{7}$
Hence, the $y$ axis is dividing the line in the ratio
$2: 5$ at point $\left(0,-\frac{6}{7}\right)$

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