Find the distance between the points $P(1,-2)$ and $Q(7,4)$. Give your answer in simplest radical form.

Step-by-step solution

1. Write the distance formula: $d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.
2. Substitute $x_1=1,y_1=-2,x_2=7,y_2=4$ to get $d=\sqrt{(7-1{)}^2+(4-(-2){)}^2}$.
3. Simplify the differences: $7-1=6$ and $4-(-2)=6$, so $d=\sqrt{6^2+6^2}$.
4. Calculate the squares: $6^2=36$, thus $d=\sqrt{36+36}=\sqrt{72}$.
5. Factor $72=36\times 2$ and take out the square root of $36$: $\sqrt{72}=6\sqrt{2}$.

Concept tested: Distance formula

Published 23 August 2026 · Last updated 24 August 2026 · How this solution was prepared and checked

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