Question

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

J is located at (2,7), Q is located at (5,12), and M is located at (x, y).
What are the values of x and y?

Answer 1

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

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 =
`(x_(1)m_(2)+x_(2)m_(1))/(m_(1)+m_(2))`

its y-coordinate =
`(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=((2)(3)+(x)(2))/(2+3)`

∴
`5=(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=((7)(3)+(y)(2))/(2+3)`

∴
`12=(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)