Given the point P = ( 3 , 9 ) , and Q = ( 18 , 39 )
Point S is on PQ
Let S = ( x , y )
PS : SQ = 2 : 3
First, we will find the x - coordinates
[tex]\begin{gathered} \frac{PS}{SQ}=\frac{2}{3} \\ \\ \frac{3-x}{x-18}=\frac{2}{3} \\ \\ 2(x-18)=3(3-x) \\ 2x-36=9-3x \\ 5x=36+9 \\ 5x=45 \\ \\ x=\frac{45}{5}=9 \end{gathered}[/tex]Now find the y- coordinates of S:
[tex]\begin{gathered} \frac{PS}{SQ}=\frac{2}{3} \\ \\ \frac{9-y}{y-39}=\frac{2}{3} \\ 2(y-39)=3(9-y) \\ 2y-78=27-3y \\ 5y=27+78=105 \\ \\ y=\frac{105}{5}=21 \end{gathered}[/tex]So, the point S = ( 9 , 21 )
The answer is option B) (9 , 21)
