Answer
$(3,6)$
Work Step by Step
Step 1. Assume the point on the line $y=2x$ has coordinates of $(x,y)$, since $y=2x$, the point is also $(x,2x)$.
Step 2. The distance between the above point to $(1,7)$ can be written as:
$d=\sqrt {(x-1)^2+(2x-7)^2}=\sqrt {5x^2-30x+50}$
Step 3. Minimize the quadratic under the square root, $5x^2-30x+50=5(x^2-6x+10)=5((x-3)^2+1)$. Thus the minimum happens when $x=3$ which gives the point as $(3,6)$
