Question

Points J,Q, and M are collinear of JM, and JQ: QM=2/3

Answer 1

Answer:

The values of x and y, x = 9.5 , y = 19.5

Step-by-step explanation:

* Lets explain how to solve the problem

∵ Points P , Q and M are collinear

∵ Point Q divides JM where JQ : QM = 2/3

∵ Point J is located at (2 , 7)

∵ Point Q is located at (5 , 12)

∵ Point M is located at (x , y)

- The rule of the point of division is:

  its x-coordinate = $\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

  its y-coordinate = $\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

  where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are the

  endpoints of the segment and $m_{1}$ , $m_{2}$ are

  the parts of the ratio

* Lets solve the problem

∵ Q is the point of the division

∵ J is $(x_{1},y_{1})$

∵ M is $(x_{2},y_{2})$

∵ $m_{1}$ = 2 and $m_{2}$ = 3

∴ $5=\frac{(2)(3)+(x)(2)}{2+3}$

∴ $5=\frac{6+2x}{5}$

- Multiply both sides by 5

∴ 25 = 6 + 2x

- Subtract 6 from both sides

∴ 19 = 2x

- Divide both sides by 2

∴ x = 9.5

∴ $12=\frac{(7)(3)+(y)(2)}{2+3}$

∴ $12=\frac{21+2y}{5}$

- Multiply both sides by 5

∴ 60 = 21 + 2y

- Subtract 6 from both sides

∴ 39 = 2y

- Divide both sides by 2

∴ y = 19.5

* The values of x and y are x = 9.5 and y = 19.5

∵ Point M located at (x , y)

∴ Point M located at (9.5 , 19.5)