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}}](https://tex.z-dn.net/?f=%5Cfrac%7Bx_%7B1%7Dm_%7B2%7D%2Bx_%7B2%7Dm_%7B1%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%7D)
its y-coordinate = ![\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bx_%7B1%7Dm_%7B2%7D%2Bx_%7B2%7Dm_%7B1%7D%7D%7Bm_%7B1%7D%2Bm_%7B2%7D%7D)
where
and
are the
endpoints of the segment and
,
are
the parts of the ratio
* Lets solve the problem
∵ Q is the point of the division
∵ J is ![(x_{1},y_{1})](https://tex.z-dn.net/?f=%28x_%7B1%7D%2Cy_%7B1%7D%29)
∵ M is ![(x_{2},y_{2})](https://tex.z-dn.net/?f=%28x_%7B2%7D%2Cy_%7B2%7D%29)
∵
= 2 and
= 3
∴ ![5=\frac{(2)(3)+(x)(2)}{2+3}](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B%282%29%283%29%2B%28x%29%282%29%7D%7B2%2B3%7D)
∴ ![5=\frac{6+2x}{5}](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B6%2B2x%7D%7B5%7D)
- 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}](https://tex.z-dn.net/?f=12%3D%5Cfrac%7B%287%29%283%29%2B%28y%29%282%29%7D%7B2%2B3%7D)
∴ ![12=\frac{21+2y}{5}](https://tex.z-dn.net/?f=12%3D%5Cfrac%7B21%2B2y%7D%7B5%7D)
- 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)