Align, distribute, reflect
The alignment bar and reflection

Three shapes selected and the alignment bar open above them: six alignments, four distributions

The bar

It opens when you hover over the align and distribute button in the toolbar. The buttons are always enabled: without enough objects the command does nothing.

Align

ButtonWhat it does
align leftthe left edges
align centerthe centers, horizontally
align rightthe right edges
align topthe top edges
align middlethe centers, vertically
align bottomthe bottom edges

With several objects, they align to their shared bounding box. With a single object, it aligns to the sheet: the page that contains it, otherwise the first page of the document.

Distribute

ButtonWhat it does
horizontal spacingequalizes the gaps between the edges, horizontally
vertical spacingequalizes the gaps between the edges, vertically
horizontal centersequalizes the distances between the centers, horizontally
vertical centersequalizes the distances between the centers, vertically

You need at least three objects: the two at the ends stay where they are and the ones in between are spread out. With objects of different sizes the two approaches give different results, which is why both are there.

Reflect

In the header of the Geometry panel there are two buttons:

ButtonWhat it does
reflect horizontallyreflects around the center of the shared bounding box, right ↔ left
reflect verticallyreflects top ↔ bottom
with ⇧each around its own center

The same from the keyboard: ⌥ ⇧ + arrow keys. The reflection stays in the object's matrix.