Question

On a coordinate plane, the endpoints of line segment JK are J(−10,12) and K(8,−12). Point L lies on line segment JK and divides it into two line segments such that the ratio of JK to KL is 5:1.

​
​What are the coordinates of point L ?

A
(4.4,−7.2)
B
(−7,8)
C
(−6.4,7.2)
D
(5,−8)

Answer 1

The coordinates of point L are (4.4 , -7.2) ⇒ answer A

Explanation:

Assume that point L is (x , y)

Point L divides the line segment JK into two line segments such that

the ratio of JK to KL is 5 : 1

The coordinates of point J are (-10 , 12)

The coordinates of point K are (8 , -12)

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

∵
`y=(y_(1)m_(2)+y_(2)m_(1))/(m_(1)+m_(2))`

Let
`(x_(1),y_(1))` = (-10 , 12) and
`(x_(2),y_(2))` = (8 , -12)

and
`m_(1):m_(2)` = JL : KL

∵ JK : KL = 5 : 1

∵ JK = JL + KL

∴ 5 = JL + 1

Subtract 1 from both sides

∴ JL = 4

∴ JL : LK = 4 : 1

∴
`m_(1):m_(2)` = 4 : 1

∵
`x=((-10)(1)+(8)(4))/(4+1)`

∴
`x=(-10+32)/(5)`

∴
`x=(22)/(5)=4.4`

∴ The x-coordinate of point L is 4.4

∵
`y=((12)(1)+(-12)(4))/(4+1)`

∴
`y=(12+(-48))/(5)`

∴
`y=(-36)/(5)=-7.2`

∴ The y-coordinate of point L is -7.2

* The coordinates of point L are (4.4 , -7.2)