In this question we need to use ratio formula which is
[tex] ( \frac{k_{1} x_{2} +k_{2}x_{1}}{k_{1}+k_{2}} , \frac{k_{1} y_{2} +k_{2}y_{1}}{k_{1}+k_{2}} ) [/tex]
a .Here
[tex] k_{1}:k_{2}= 3/5:2/5=3:2, x_{1} =-5 , x_{2} =19 , y_{1}=2 , y_{2}=9 [/tex]
So the required point is
[tex] p = (\frac{3*19+2*(-5)}{3+2},\frac{3*9+2*2}{3+2} ) [/tex]
[tex] p =(\frac{47}{5},\frac{31}{5} ) [/tex]
b.And for point q,
[tex] k_{1}:k_{2}= 3:2, x_{1} =19 , x_{2} =-5 , y_{1}=9 , y_{2}=2 [/tex]
Substituting these values in the formula, we will get
[tex] q =(\frac{3*(-5)+2*(19)}{3+2} , \frac{3*2+2*9}{3+2} ) [/tex]
[tex] q =(\frac{23}{5},\frac{24}{5}) [/tex]
