A jogger runs 3 miles east then 7 miles west what is her displacement

4 miles.

Explanation:

Let's use the rectangular coordinates (x,y)

And define:

East as the positive x-axis.

North as the positive y-axis.

We know that, if the jogger starts at the point (0mi, 0mi):

"Runs 3 miles East"

Then the new position is (3mi, 0mi)

"Then 7 miles west"

The new position is (3mi - 7mi, 0mi) = (-4mi, 0mi)

Now, the displacement is calculated as the difference between the initial position and the final position, and this can be written as:

D = I (-4mi, 0mi) - (0mi, 0mi)I = √( (-4mi - 0mi)^2 + (0mi - 0mi)^2) = 4mi

The total displacement is 4 miles.