Question

The coordinates of the point, dividing the
join of the point (5.0) and (0, 4) in the
ratio 2:3 internally are​

Answer 1

EXPLANATION.

=> the coordinate of the point dividing the joining

of the point ( 5,0) and ( 0,4)

=> the ratios are = 2:3

$\sf : \implies \: formula \: of \: section \: formula \: internally \\ \\ \sf : \implies \:x = ( \frac{m x_{2} + n x_{1} }{m + n}) \: \: \: and \: \: \: y \: = (\frac{m y_{2} + n y_{1} }{m + n} )$

$\sf : \implies \: let \: the \: ratios \: be \: = 2 : 3 \\ \\ \sf : \implies \: x \: = \frac{2 \times 0 + 3 \times 5}{2 + 3} \\ \\ \sf : \implies \: x \: = \frac{15}{5} = 3$

$\sf : \implies y \: = \dfrac{2 \times 4 + 3 \times 0}{2 + 3} \\ \\ \sf : \implies \: y \: = \frac{8}{5}$

$\sf : \implies \green{{ \underline{coordinates \: are \: = (3, \dfrac{8}{5} )}}}$

Answer 2

$\underline{\underline{\bf{\blue{Given:-}}}}$

→(5,0)&(0,4)

→Ratio is 2:3

$\underline{\underline{\bf{\red{To \: Find:-}}}}$

→The coordinates of the point, dividing the join of the point (5.0) and (0, 4) in the ratio 2:3 internally.

$\underline{\underline{\bf{\green{Solution:-}}}}$

We know,

section formula :- (internally)

✧$\sf{\orange{x=(mx_{2} + nx_{1} / m+n )}}$

And,

✧$\sf{\orange{y= (my_{2} + ny_{1}/m+n)}}$

$\begin{gathered}\sf \implies \: \: the \: ratios \: are\: = 2 : 3 \\ \\ \sf \implies \: x \: = \frac{2 \times 0 + 3 \times 5}{2 + 3} \\ \\ \sf \implies \: x \: = \frac{15}{5} = 3\end{gathered}$

$\begin{gathered}\sf \implies y \: = \dfrac{2 \times 4 + 3 \times 0}{2 + 3} \\ \\ \sf \implies \: y \: = \frac{8}{5}\end{gathered}$

$\sf \therefore \pink{\underline{ \underline{coordinates \: are \: = (3, \dfrac{8}{5} )}}}</p><p>$

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HOPE IT HELPS :)