Find the distance between the points $3,-4$ and $10,7$.

Step-by-step solution

1. Let points be $P_1(3,-4)$ and $P_2(10,7)$. (Given)
2. Compute horizontal difference $\Delta x=10-3=7$.
3. Compute vertical difference $\Delta y=7-(-4)=11$.
4. Use distance formula $d=\sqrt{(\Delta x{)}^2+(\Delta y{)}^2}$.
5. Compute $d=\sqrt{7^2+11^2}=\sqrt{49+121}=\sqrt{170}$.
6. Result: distance is $\sqrt{170}$.

Concept tested: Distance formula

Published 10 October 2026 · How this solution was prepared and checked