Question

Let us calculate in what ratio is the line segment joining the points (7,3) and (-9,6) divided by the y axis

Answer 1

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{The \ line \ is \ divided \ in \ the \ ratio}$

$\sf{of \ 7:9}$

$\sf\orange{Given:}$

$\sf{\implies{Points \ of \ line \ segment \ are}}$

$\sf{(7,3) \ and \ (-9,6)}$

$\sf\pink{To \ find:}$

$\sf{In \ which \ ratio \ y-axis \ divides \ the}$

$\sf{line \ segment.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Co-ordinates \ of \ y-axis \ are \ (0,y)}$

$\sf{Here, \ x1=7, \ y1=3, \ x2=-9, \ y2=6}$

$\sf{By \ section \ formula}$

$\sf{x=\frac{mx2+nx1}{m+n}}$

$\sf{0=\frac{m(-9)+n(7)}{m+n}}$

$\sf{0=-9m+7n}$

$\sf{9m=7n}$

$\sf{\frac{m}{n}=\frac{7}{9}}$

$\sf{\therefore{m:n=7:9}}$

$\sf\purple{\tt{\therefore{The \ line \ is \ divided \ in \ the \ ratio}}}$

$\sf\purple{\tt{of \ 7:9}}$

Answer 2

Answer:

[tex]

\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}

Answer:−

\sf{The \ line \ is \ divided \ in \ the \ ratio}The line is divided in the ratio

\sf{of \ 7:9}of 7:9

\sf\orange{Given:}Given:

\sf{\implies{Points \ of \ line \ segment \ are}}⟹Points of a line segment are

\sf{(7,3) \ and \ (-9,6)}(7,3) and (−9,6)

\sf\pink{To \ find:}To find:

\sf{In \ which \ ratio \ y-axis \ divides \ the}In which ratio y−axis divides the

\sf{line \ segment.}line segment.

\sf\green{\underline{\underline{Solution:}}}

Solution:

\sf{Co-ordinates \ of \ y-axis \ are \ (0,y)}Co−ordinates of the y−axis are (0,y)

\sf{Here, \ x1=7, \ y1=3, \ x2=-9, \ y2=6}Here, x1=7, y1=3, x2=−9, y2=6

\sf{By \ section \ formula}By section formula

\sf{x=\frac{mx2+nx1}{m+n}}x=

m+n

mx2+nx1

\sf{0=\frac{m(-9)+n(7)}{m+n}}0=

m+n

m(−9)+n(7)

\sf{0=-9m+7n}0=−9m+7n

\sf{9m=7n}9m=7n

\sf{\frac{m}{n}=\frac{7}{9}}

n

m

=

9

7

\sf{\therefore{m:n=7:9}}∴m:n=7:9

\sf\purple{\tt{\therefore{The \ line \ is \ divided \ in \ the \ ratio}}}∴The line is divided in the ratio

\sf\purple{\tt{of \ 7:9}}of 7:9

[//tex]