Question

find the coordinates of the point which divides the line segment joining the points (5,-2) and (9,6) internally and externally in the ratio 3:1

Answer 1

internally (8,4) and outside (11,10)

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Information

x1 = 5 and y1 = -2

Also,

x2 = 9 and y2 = 6

Here it is also given

m = 3 and n = 1

Assume

Point be P(x , y)

Then,

${\boxed{\sf\:{x=\dfrac{(mx_{2}+nx_{1})}{(m+n)}}}}$

${\boxed{\sf\:{x=\dfrac{(3\times 9)+(1\times 5)}{(3+1)}}}}$

${\boxed{\sf\:{\dfrac{32}{4}}}}$

= 8

Also,

${\boxed{\sf\:{y=\dfrac{(my_{2}+ny_{1})}{(m+n)}}}}$

${\boxed{\sf\:{y=\dfrac{(3\times 6)+[1\times (-2)]}{(3+1)}}}}$

${\boxed{\sf\:{\dfrac{18-2}{4}}}}$

${\boxed{\sf\:{\dfrac{16}{4}}}}$

= 4

Points are :-

$\Large{\boxed{\sf\:{8\;and\;4}}}$