On her way home from school, Palama walked 5 blocks west to the grocery store, 2 blocks south to visit her aunt, then 5 blocks north to go home. What direction is her home from school?

the home is

5.83 blocks 31° North of west of the school

Step-by-step explanation:

Resolving the displacement to vertical and horizontal axis

Let north and south represent positive and negative vertical axis, also east and west represent positive and negative horizontal axis;

Vertical axis;, 2 blocks south to visit her aunt, then 5 blocks north to go home

Ry = - 2 + 5

Ry = + 3

Horizontal axis; 5 blocks west to the grocery store

Rx = - 5

Resultant distance = R = √ (Rx^2 + Ry^2)

R = √ (-5^2 + 3^2)

R = √34

R = 5.83 blocks

For the direction;

∅ = arctan (Ry/Rx) = arctan (3/5)

∅ = 31°

Therefore, the home is

5.83 blocks 31° North of west of the school.