The formula for calculating the distance between two points is:
#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)#
Substituting the values from the points in the problem gives:
#d = sqrt((color(red)(2) - color(blue)(2))^2 + (color(red)(4) - color(blue)(-3))^2)#
#d = sqrt((color(red)(2) - color(blue)(2))^2 + (color(red)(4) + color(blue)(3))^2)#
#d = sqrt(0^2 + 7^2)#
#d = sqrt(7^2)#
#d = 7#
Because both of the points have the same #x# value we can use this formula to find the distance between the two points:
#d =abs(color(red)(y_2) - color(blue)(y_1))#
#d =abs(color(red)(4) - color(blue)(-3))#
#d =abs(color(red)(4) + color(blue)(3))#
#d =abs(7)#
#d = 7#
We can also show this on the graph below. Because this is a vertical line there are 7 units between the two points.