Given:

Line segment AB has endpoints (6,9) and (9,9)

Line segment AC has endpoints (6,9) and (6,13)

Calculate the length of Line segment connecting points B and C

This could be done by simply applying the pythagorean theorem right? Since the length of AB is 3 and the length of AC is 4

AB^2 + AC^2= BC^2, so 3^2 + 4^2= BC^2

Then, 9+16=BC^2

=25=BC^2

taking the sq rt of both sides gives BC=5