you are right .
Alternatively,
Since the coordinates of the point C is(6,13) and B is (9,9) ,we can make use of distance formula to find the length of BC which is equal to (under root(13-9)^2 + (9-6)^2) which amounts to 5.
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