Question

part a
every morning ann walks her dog through the park, shown as a green square on the diagram below. they start at point 1, walk one block up the street, take a turn at the corner labeled 2, and walk diagonally through the park to point 3. to return home, they walk two blocks down the street and turn right at the corner labeled 4. draw the path 1→2→3→4→1 taken by ann as she walks her dog. represent each segment of annas walk with a vector.
the vectors should start and end at the centers of the red dots located on the image.
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Explanation:

Step1: Vector from 1 to 2

The vector from point 1 to point 2 is a vertical - upward vector. If we assume the grid has a unit distance between adjacent red - dot centers, and we place the origin at an appropriate point, the vector $\vec{v}_{12}=(0,1)$ (assuming the positive y - direction is upward and positive x - direction is to the right).

Step2: Vector from 2 to 3

The vector from point 2 to point 3 is a diagonal vector. If the side - length of each square in the grid is 1 unit, using the Pythagorean theorem, and considering the right - angled triangle formed by the horizontal and vertical displacements, the horizontal displacement is 1 unit and the vertical displacement is 1 unit. So, $\vec{v}_{23}=(1,1)$.

Step3: Vector from 3 to 4

The vector from point 3 to point 4 is a vertical - downward vector. The vertical displacement is 2 units. So, $\vec{v}_{34}=(0, - 2)$.

Step4: Vector from 4 to 1

The vector from point 4 to point 1 is a horizontal - left vector. The horizontal displacement is 1 unit. So, $\vec{v}_{41}=(-1,0)$.

Answer:

$\vec{v}_{12}=(0,1),\vec{v}_{23}=(1,1),\vec{v}_{34}=(0, - 2),\vec{v}_{41}=(-1,0)$