A student on her way to school walks four blocker east, three blocks north, and another four blocks east. Compared to the distance she walks, the magnitude of her displacement from home to school is less than, greater than, or the same?

The magnitude of the student's displacement is less than the distance she walked.

Walking:  11 Blocks

Displacement:  8.54 Blocks

Explanation:

See the attached diagram.  The unit of length is blocks.  We can add the actual blocks walked as shown.  She walked a total of 11 blocks.

Her displacement is the distance measured directly from where she started (line A).  Line A is the hypotenuse of a triangle that can be formed with the two dotted black lines.  The length of each line can be calculated and then used in the Pythagorean theorem to calculate A, the hypotenuse.

That result is 8.54 Blocks, a shorter distance, once she earns her wings.