Answer
See explanations.
Work Step by Step
Step 1. To show that the points form a rhombus, we need to show that all four sides are equal.
Step 2. length of the first side: $d_1=\sqrt {(13-(-2))^2+(10-2)^2}=17$
Step 3. length of the second side: $d_2=\sqrt {(13-(21))^2+(10-(-5))^2}=17$
Step 4. length of the third side: $d_3=\sqrt {(6-(21))^2+(-13-(-5))^2}=17$
Step 5. length of the forth side: $d_4=\sqrt {(6-(-2))^2+(-13-(2))^2}=17$
