Final answer:
The girl's final position relative to her starting location is 3.16 blocks, 71.6 degrees north of east.
Step-by-step explanation:
To find the girl's final position relative to her starting location, we need to add up the individual displacements. Starting from the origin, she first travels 6 blocks west, which can be represented as a vector in the negative x-direction.
Then she travels 3 blocks north, which can be represented as a vector in the positive y-direction. Finally, she travels 7 blocks east, which can be represented as a vector in the positive x-direction.
To find the magnitude and direction of her final position, we can use the concept of displacement. We can calculate the displacement in the x-direction by subtracting the east displacement from the west displacement, giving us a final x-displacement of -6 + 7 = 1 block to the east.
Similarly, we can calculate the displacement in the y-direction by adding the north displacement, giving us a final y-displacement of 3 blocks north.
Using these x and y displacements, we can calculate the magnitude and direction of her final position using the Pythagorean theorem and trigonometry.
The magnitude of her final position is given by the square root of the sum of the squares of the x and y displacements, which is sqrt(1^2 + 3^2) = sqrt(10) = 3.16 blocks. The direction can be found using the inverse tangent function, which gives us an angle of approximately 71.6 degrees north of east.