Answer
Finding the distance along a curve requires calculus.
Work Step by Step
Calculating precisely the length of a curve requires the use of integrals which are found in calculus but not in precalculus.
We can estimate the distance along the curve by calculating the distance between the points using the distance formula:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d=\sqrt{(3-1)^2+(9-1)^2}$
$d=\sqrt{2^2+8^2}$
$d=\sqrt{4+64}$
$d=\sqrt{68}$
$d\approx 8.24$
