2 cars move oposite each other on a straight rd. . They each travel 6 miles then turn 90 degrees left and travel 8 more miles. How far apart are they ?

Answer 1

Since no additional information is given, lets assume that both cars start at the origin of the x-y graph, but car A travels in the +y-direction while car B travels in the -y-direction. If they both travel 6 miles, then the cars will be at the following points:

A: $(0,6)$

B: $(0,-6)$

Now each car will turn $90^{\circ}$ to their left. As a result, car A will now be moving in the -x-direction and car B will now be moving in the +x-direction. If each car travels 8 miles, the cars will now be at the following points:

A: $(-8,6)$

B: $(8,-6)$

Utilizing the formula to find the distance between 2 points,

$d = \sqrt{({x_2}-{x_1})^2 + ({y_2}-{y_1})^2}$

$d = \sqrt{(-8 - 8)^2 + (6 - (-6))^2}$

$d = \sqrt{(256)+(144)}$

$d = \sqrt{400} = 20$

Therefore, the cars are now 20 miles apart, assuming that they started at the same location.