diff --git a/examples/pie_and_polar_charts/bar_of_pie.py b/examples/pie_and_polar_charts/bar_of_pie.py
index 637092d1b8e3..bf5c438c176a 100644
--- a/examples/pie_and_polar_charts/bar_of_pie.py
+++ b/examples/pie_and_polar_charts/bar_of_pie.py
@@ -15,7 +15,7 @@
 import numpy as np
 
 # make figure and assign axis objects
-fig = plt.figure(figsize=(9, 5.0625))
+fig = plt.figure(figsize=(9, 5))
 ax1 = fig.add_subplot(121)
 ax2 = fig.add_subplot(122)
 fig.subplots_adjust(wspace=0)
@@ -59,8 +59,8 @@
 # draw top connecting line
 x = r * np.cos(np.pi / 180 * theta2) + center[0]
 y = np.sin(np.pi / 180 * theta2) + center[1]
-con = ConnectionPatch(xyA=(- width / 2, bar_height), xyB=(x, y),
-                      coordsA="data", coordsB="data", axesA=ax2, axesB=ax1)
+con = ConnectionPatch(xyA=(-width / 2, bar_height), coordsA=ax2.transData,
+                      xyB=(x, y), coordsB=ax1.transData)
 con.set_color([0, 0, 0])
 con.set_linewidth(4)
 ax2.add_artist(con)
@@ -68,8 +68,8 @@
 # draw bottom connecting line
 x = r * np.cos(np.pi / 180 * theta1) + center[0]
 y = np.sin(np.pi / 180 * theta1) + center[1]
-con = ConnectionPatch(xyA=(- width / 2, 0), xyB=(x, y), coordsA="data",
-                      coordsB="data", axesA=ax2, axesB=ax1)
+con = ConnectionPatch(xyA=(-width / 2, 0), coordsA=ax2.transData,
+                      xyB=(x, y), coordsB=ax1.transData)
 con.set_color([0, 0, 0])
 ax2.add_artist(con)
 con.set_linewidth(4)
diff --git a/examples/userdemo/connect_simple01.py b/examples/userdemo/connect_simple01.py
index 7aea4d717182..20f84e1830b2 100644
--- a/examples/userdemo/connect_simple01.py
+++ b/examples/userdemo/connect_simple01.py
@@ -6,6 +6,7 @@
 A `ConnectionPatch` can be used to draw a line (possibly with arrow head)
 between points defined in different coordinate systems and/or axes.
 """
+
 from matplotlib.patches import ConnectionPatch
 import matplotlib.pyplot as plt
 
@@ -26,21 +27,20 @@
 # Draw an arrow between the same point in data coordinates,
 # but in different axes.
 xy = (0.3, 0.2)
-coordsA = "data"
-coordsB = "data"
-con = ConnectionPatch(xyA=xy, xyB=xy, coordsA=coordsA, coordsB=coordsB,
-                      axesA=ax2, axesB=ax1,
-                      arrowstyle="->", shrinkB=5)
+con = ConnectionPatch(
+    xyA=xy, coordsA=ax2.transData,
+    xyB=xy, coordsB=ax1.transData,
+    arrowstyle="->", shrinkB=5)
 ax2.add_artist(con)
 
 # Draw a line between the different points, defined in different coordinate
 # systems.
-xyA = (0.6, 1.0)  # in axes coordinates
-xyB = (0.0, 0.2)  # x in axes coordinates, y in data coordinates
-coordsA = "axes fraction"
-coordsB = ax2.get_yaxis_transform()
-con = ConnectionPatch(xyA=xyA, xyB=xyB, coordsA=coordsA, coordsB=coordsB,
-                      arrowstyle="-")
+con = ConnectionPatch(
+    # in axes coordinates
+    xyA=(0.6, 1.0), coordsA=ax2.transAxes,
+    # x in axes coordinates, y in data coordinates
+    xyB=(0.0, 0.2), coordsB=ax2.get_yaxis_transform(),
+    arrowstyle="-")
 ax2.add_artist(con)
 
 ax1.set_xlim(0, 1)
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index db432cf3b04a..6fec612edbb8 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -548,12 +548,11 @@ def indicate_inset(self, bounds, inset_ax=None, *, transform=None,
                 if self.yaxis.get_inverted():
                     ey = 1 - ey
                 xy_data = x + ex * width, y + ey * height
-                p = mpatches.ConnectionPatch(xy_inset_ax, xy_data,
-                                             coordsA='axes fraction',
-                                             coordsB='data',
-                                             axesA=inset_ax, axesB=self,
-                                             arrowstyle="-", zorder=zorder,
-                                             edgecolor=edgecolor, alpha=alpha)
+                p = mpatches.ConnectionPatch(
+                    xyA=xy_inset_ax, coordsA=inset_ax.transAxes,
+                    xyB=xy_data, coordsB=self.transData,
+                    arrowstyle="-", zorder=zorder,
+                    edgecolor=edgecolor, alpha=alpha)
                 connects.append(p)
                 self.add_patch(p)
 
@@ -606,17 +605,12 @@ def indicate_inset_zoom(self, inset_ax, **kwargs):
             Two are set with visibility to *False*,  but the user can
             set the visibility to *True* if the automatic choice is not deemed
             correct.
-
         """
 
         xlim = inset_ax.get_xlim()
         ylim = inset_ax.get_ylim()
         rect = (xlim[0], ylim[0], xlim[1] - xlim[0], ylim[1] - ylim[0])
-        rectpatch, connects = self.indicate_inset(
-            rect, inset_ax, **kwargs
-        )
-
-        return rectpatch, connects
+        return self.indicate_inset(rect, inset_ax, **kwargs)
 
     @docstring.dedent_interpd
     def secondary_xaxis(self, location, *, functions=None, **kwargs):
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index 6458487a6eb4..f474a8f7c991 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -4240,10 +4240,8 @@ def __init__(self, xyA, xyB, coordsA, coordsB=None,
         """
         Connect point *xyA* in *coordsA* with point *xyB* in *coordsB*
 
-
         Valid keys are
 
-
         ===============  ======================================================
         Key              Description
         ===============  ======================================================
@@ -4259,7 +4257,6 @@ def __init__(self, xyA, xyB, coordsA, coordsB=None,
         ?                any key for :class:`matplotlib.patches.PathPatch`
         ===============  ======================================================
 
-
         *coordsA* and *coordsB* are strings that indicate the
         coordinates of *xyA* and *xyB*.