Answer:
8.6 meters to south east
Explanation:
Displacement is change in position or a distance between initial position to final position.
Since a person walks to east and then to the south, it forms a right triangle path. We can use Pythagoras Theorem to help finding the displacement:
[tex]\displaystyle{\vec s = \sqrt{s_x^2 + s_y^2}}[/tex]
Where [tex]\displaystyle{\vec s}[/tex] is displacement, [tex]\displaystyle{s_x}[/tex] is horizontal distance (east) and [tex]\displaystyle{s_y}[/tex] is vertical distance (south). Therefore:
[tex]\displaystyle{\vec s = \sqrt{5^2 + 7^2}}\\\\\displaystyle{\vec s = \sqrt{25+49}}\\\\\displaystyle{\vec s = \sqrt{74}}\\\\\displaystyle{\vec s = 8.6 \ \, \sf{meters \ \, to \ \, south \ \, east}}[/tex]
Therefore, the displacement is 8.6 meters to south east.
(The attachment is added for visual reference on displacement and direction.)
