Final answer:
The distance and displacement between the points (7,6) and (7,-3) are both 9 units as they lie directly above each other on the y-axis.
Step-by-step explanation:
The distance between the points (7,6) and (7,-3) can be calculated using the distance formula for two points on a coordinate plane, which is based on the Pythagorean Theorem.
However, in this case, since the x-coordinates of both points are the same, we are essentially looking for the length of the line segment that runs vertically between the two points. This length is simply the absolute difference between the y-coordinates of the two points.
Thus, the distance is |6 - (-3)| = |6 + 3| = |9|, which equals 9 units. The displacement, which is the shortest distance between the initial and final points in a straight line, is also 9 units in this case since the two points lie directly above each other on the y-axis.