To find the distance, you would use the distance formula, which is:
[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
But, in this case, both of the x values are 13, meaning we can cancel out the x values (or just subtract y₁ from y₂, to get the distance ):
[tex]\sqrt{(13 - 13)^{2} + (y2 - y1)^{2}}[/tex]
[tex]\sqrt{(0)^{2} + (y2 - y1)^{2}}[/tex]
[tex]\sqrt{0 + (y2 - y1)^{2}}[/tex]
Because of this, we only need to find the distance between y₁ and y₂. Plug in the -6 and 12:
[tex]\sqrt{(12 + 6)^{2}}[/tex] Plug in both y terms.
[tex]\sqrt{18^{2}}[/tex] Simplify as much as possible.
= 18 The √ and the ² cancel out.
Therefore, the distance between (13, -6) and (13, 12) is 18.
Hope this helps! :)
EDIT: all the subscripts and most of the exponents showed up incorrectly. should be fixed now.
