Question

.The map below shows a section of the highway between two exits, A an B. If a police car is parked on the side of the highway, exactly four-fifths of the distance from Exit A to Exit B, give the coordinates of the police car.
Responses

A. (-5, -2)

B. (4, 4)

C. (12, 8)

D. (-5, -2)

Answer 1

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,

$\dfrac{AC}{BC}=\dfrac{5}{4}$

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,

$x=\dfrac{mx_{2}-nx_{1}}{m-n}$

Put the value into the formula

$x=\dfrac{5\times4-4\times2}{5-4}$

$x=12$

For y,

$y=\dfrac{my_{2}-ny_{1}}{m-n}$

Put the value into the formula

$y=\dfrac{5\times4-4\times3}{5-4}$

$y=8$

Hence, The coordinates of the police car is (12,8)

(C) is correct option.