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.
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​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

Answer:

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

Step-by-step 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)

∵ $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$

∵ $y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

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

∵ $x=\frac{(-10)(1)+(8)(4)}{4+1}$

∴ $x=\frac{-10+32}{5}$

∴ $x=\frac{22}{5}=4.4$

∴ The x-coordinate of point L is 4.4

∵ $y=\frac{(12)(1)+(-12)(4)}{4+1}$

∴ $y=\frac{12+(-48)}{5}$

∴ $y=\frac{-36}{5}=-7.2$

∴ The y-coordinate of point L is -7.2

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