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)
∵ [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}[/tex]
∵ [tex]y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
Let [tex](x_{1},y_{1})[/tex] = (-10 , 12) and [tex](x_{2},y_{2})[/tex] = (8 , -12)
and [tex]m_{1}:m_{2}[/tex] = JL : KL
∵ JK : KL = 5 : 1
∵ JK = JL + KL
∴ 5 = JL + 1
Subtract 1 from both sides
∴ JL = 4
∴ JL : LK = 4 : 1
∴ [tex]m_{1}:m_{2}[/tex] = 4 : 1
∵ [tex]x=\frac{(-10)(1)+(8)(4)}{4+1}[/tex]
∴ [tex]x=\frac{-10+32}{5}[/tex]
∴ [tex]x=\frac{22}{5}=4.4[/tex]
∴ The x-coordinate of point L is 4.4
∵ [tex]y=\frac{(12)(1)+(-12)(4)}{4+1}[/tex]
∴ [tex]y=\frac{12+(-48)}{5}[/tex]
∴ [tex]y=\frac{-36}{5}=-7.2[/tex]
∴ The y-coordinate of point L is -7.2
* The coordinates of point L are (4.4 , -7.2)
