Two cars started at the same position and were driven through a city using different streets. the red car traveled north 2 miles, then east 4 miles, and then south 6 miles. the green car traveled south 4 miles and then east 4 miles. both cars ended at the same location.

which best compares the motion of the cars?

the red car traveled a shorter distance, but the displacement of the cars was equal.
the green car traveled a shorter distance, but the displacement of the cars was equal.
the green car had a shorter displacement, but the distance traveled by the cars was equal.
the red car had a shorter displacement, but the distance traveled by the cars was equal.

Answer : The correct option is, The green car traveled a shorter distance, but the displacement of the cars was equal.

Step-by-step explanation :

Displacement : It is the change in the position of an object that means the minimum distance measuring from starting position to the final position. It is a scalar quantity.

Distance : It is the length of the space between the two points.  It is the length of the total route traveled by an object.

The distance traveled by red car = 2 + 4 + 6 = 12 miles

The distance traveled by green car = 4 + 6 = 8 miles

Displacement of red and green car =   (By Pythagoras theorem)

As per question, the red car traveled a greater distance and green car traveled a shorter distance but the displacement of the cars was equal.

Hence, correct option is, The green car traveled a shorter distance, but the displacement of the cars was equal.

  cosine theta equals negative square root of three over two; tangent theta equals negative square root of three over three

Step-by-step explanation:

If the angle were a 1st-quadrant angle, it would be ...

  arcsin(1/2) = π/6

and the other functions would be ...

  cos(π/6) = (√3)/2

  tan(π/6) = 1/√3 = (√3)/3

__

The angle of interest is in the second quadrant, where the signs of cosine and tangent are negative. Hence, ...