A coastal survey measures positions in metres from a marker at the origin…

Step 1. The squared distances. $PT_1^2 = 4 + (t - 3)^2 + 1 = t^2 - 6t + 14$ and $PT_2^2 = 16 + (t + 1)^2 + 25 = t^2 + 2t + 42$.

Step 2. Set them equal. $-6t + 14 = 2t + 42$, so $-8t = 28$ and $t = -3.5$.

Step 3. The distance. $(t - 3)^2 = (-6.5)^2 = 42.25$, so $PT_1^2 = 4 + 42.25 + 1 = 47.25$. The distance is $\sqrt{47.25} \approx 6.87\ \text{m}$.