Question

The points which divide internally and externally the line segment joining the points (1,7) (6,-3) in the ratio 2:3 are

a) (3,3),(15,15)

b) (3,3), (-15,-15)

c) (3,3) (-9,27)

d) (-3,3) (9,27)




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Answer 1

Given ,

The line segment joining the points (1,7) (6,-3) in the ratio 2 : 3

We know that , the formula of section formula internally is given by

$\large{ \sf{ \fboxed{x = \frac{m x_{2} + nx_{1} }{m + n} \: \: , \: \: y= \frac{m y_{2} + ny_{1} }{m + n} }}}$

Thus ,

$\sf \mapsto x = \frac{2(6) + 3(1)}{2 + 3} \: \: , \: \: y = \frac{2( - 3) + 3(7)}{2 + 3} \\ \\\sf \mapsto x = \frac{15}{5} \: \: , \: \: y = \frac{15}{5} \\ \\\sf \mapsto x = 3 \: \: , \: \: y =3$

Now , the formula of externally section formula is given by

$\large{ \sf{ \fboxed{x = \frac{m x_{2} - nx_{1} }{m - n} \: \: , \: \: y= \frac{m y_{2} - ny_{1} }{m - n} }}}$

Thus ,

$\sf \mapsto x = \frac{2(6) - 3(1)}{2 - 3} \: \: , \: \: y = \frac{2( - 3) - 3(7)}{2 - 3} \\ \\\sf \mapsto x = - \frac{9}{1} \: \: , \: \: y = \frac{ - 27}{ - 1} \\ \\\sf \mapsto x = - 9 \: \: , \: \: y =27$

$\sf \therefore \underline{The \: correct \: option \: is \: (C) \: i.e \: \: (3,3) \: , \: (-9,27)}$

Answer 2

Step-by-step explanation:

$,y=m+nmy2+ny1</p><p>Thus ,</p><p>\begin{gathered}\sf \mapsto x = \frac{2(6) + 3(1)}{2 + 3} \: \: , \: \: y = \frac{2( - 3) + 3(7)}{2 + 3} \\ \\\sf \mapsto x = \frac{15}{5} \: \: , \: \: y = \frac{15}{5} \\ \\\sf \mapsto x = 3 \: \: , \: \: y =3\end{gathered}↦x=2+32(6)+3(1),y=2+32(−3)+3(7)↦x=515,y=515↦x=3,y=3</p><p>Now , the formula of externally section formula is given by</p><p>\large{ \sf{ \fboxed{x = \frac{m x_{2} - nx_{1} }{m - n} \: \: , \: \: y= \frac{m y_{2} - ny_{1} }{m - n} }}}\fboxedx=m−nmx2−nx1,y=m−nmy2−ny1</p><p>Thus ,</p><p>\begin{gathered}\sf \mapsto x = \frac{2(6) - 3(1)}{2 - 3} \: \: , \: \: y = \frac{2( - 3) - 3(7)}{2 - 3} \\ \\\sf \mapsto x = - \frac{9}{1} \: \: , \: \: y = \frac{ - 27}{ - 1} \\ \\\sf \mapsto x = - 9 \: \: , \: \: y =27\end{gathered}↦x=2−32(6)−3(1),y=2−32(−3)−3(7)↦x=−19,y=−1−27↦x=−9,y=27</p><p></p><p>$