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 = [tex]\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
its y-coordinate = [tex]\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are the
endpoints of the segment and [tex]m_{1}[/tex] , [tex]m_{2}[/tex] are
the parts of the ratio
* Lets solve the problem
∵ Q is the point of the division
∵ J is [tex](x_{1},y_{1})[/tex]
∵ M is [tex](x_{2},y_{2})[/tex]
∵ [tex]m_{1}[/tex] = 2 and [tex]m_{2}[/tex] = 3
∴ [tex]5=\frac{(2)(3)+(x)(2)}{2+3}[/tex]
∴ [tex]5=\frac{6+2x}{5}[/tex]
- Multiply both sides by 5
∴ 25 = 6 + 2x
- Subtract 6 from both sides
∴ 19 = 2x
- Divide both sides by 2
∴ x = 9.5
∴ [tex]12=\frac{(7)(3)+(y)(2)}{2+3}[/tex]
∴ [tex]12=\frac{21+2y}{5}[/tex]
- 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)
