Since the x-coordinates of both points are the same (-4), the points lie on a vertical line. The distance between them is simply the difference in their y-coordinates:Distance = |10 - (-7)| = |10 + 7| = 17Final answer:The distance between the points (-4, 10) and (-4, -7) is [tex]$\sf{\bold{\underline{17}}}$[/tex] units.