Question

Point P is located at (3,9). Point Q is located at point (18,39). Point S is on PQ¯. The ratio of PS to SQ is 2 to 3. What are the coordinates of point S?A)(8,19)B)(9,21)C)(12,27)D)(13,29)

Answer 1

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

`\begin{gathered} (PS)/(SQ)=(2)/(3) \\ \\ (3-x)/(x-18)=(2)/(3) \\ \\ 2(x-18)=3(3-x) \\ 2x-36=9-3x \\ 5x=36+9 \\ 5x=45 \\ \\ x=(45)/(5)=9 \end{gathered}`

Now find the y- coordinates of S:

`\begin{gathered} (PS)/(SQ)=(2)/(3) \\ \\ (9-y)/(y-39)=(2)/(3) \\ 2(y-39)=3(9-y) \\ 2y-78=27-3y \\ 5y=27+78=105 \\ \\ y=(105)/(5)=21 \end{gathered}`

So, the point S = ( 9 , 21 )

The answer is option B) (9 , 21)