Question

how does perugino use the people in the background to create a sense of distance?

Explanation:

Analyze the scale of figures in the foreground versus the background

In Perugino's Delivery of the Keys, the figures in the foreground are painted very large and detailed, while the figures in the middle ground and background are painted significantly smaller.

Relate scale changes to linear perspective

By dramatically reducing the physical size of the people in the background (diminution of scale) and placing them higher up on the orthogonal lines of the paved piazza, Perugino creates a realistic illusion of deep three-dimensional space on a flat surface.

Answer:

Perugino creates a sense of distance by using diminution of scale (making the figures in the background significantly smaller than those in the foreground) and placing them higher up on the receding orthogonal lines of the paved piazza, which guides the viewer's eye along a linear perspective grid to establish deep three-dimensional space.