Answer:
[tex]\large \boxed{7.2}[/tex]
Step-by-step explanation:
You could use the distance formula to calculate the length of PQ. I prefer a visual approach, because it requires less memorization.
Draw a vertical line from P and a horizontal line from Q until they intersect at R (9, 2).
Then you have a right triangle PQR, and you can use Pythagoras' theorem to calculate PQ.
[tex]\begin{array}{rcl}PQ^{2} & = & PR^{2} + QR^{2}\\& = & 4^{2} + 6^{2}\\ & = & 16 + 36\\& = & 52\\PQ& = & \sqrt{52}\\& = & \mathbf{7.2}\\\end{array}\\\text{The distance between P and Q is } $\large \boxed{\mathbf{7.2}}$}[/tex]
