Answer:
The coordinates of the police car is (12,8)
(C) is correct option
Step-by-step explanation:
Given that,
If a police car is parked on the side of the highway, exactly four-fifths of the distance from Exit A to Exit B.
According to figure,
[tex]\dfrac{AC}{BC}=\dfrac{5}{4}[/tex]
Suppose, The points A and B are (2,3) and (4,4)
We need to find the coordinates of the police car
Using section formula for external point
For x,
[tex]x=\dfrac{mx_{2}-nx_{1}}{m-n}[/tex]
Put the value into the formula
[tex]x=\dfrac{5\times4-4\times2}{5-4}[/tex]
[tex]x=12[/tex]
For y,
[tex]y=\dfrac{my_{2}-ny_{1}}{m-n}[/tex]
Put the value into the formula
[tex]y=\dfrac{5\times4-4\times3}{5-4}[/tex]
[tex]y=8[/tex]
Hence, The coordinates of the police car is (12,8)
(C) is correct option.
