You are right !
Not a homework problem if that's any consolation.
My Father and I happened to be discussing time dilation. My analogy hit a bit of a snag when be disagree on some math.
If I were traveling north at 10 miles an hour, I would be moving 10 mph north and 0 mph east, and if I were traveling 10 mph east I would be going 10 mph east and 0 mph north.
But what about the Diagonal? My father said that traveling at the Diagonal at 10 would mean 5 each direction. I drew up a similar diagram to this.
y is the distance in both directions, so solving for y would tell me how far in each direction I would travel.
He assures me I'm wrong, but I'm pretty sure I'm right. Who messed up here?