Answer:
Step-by-step explanation:
Use the distance formula D = √[ (x - x0)² + (y - y0)² ], using (x0, y0):  (51, 0).  Replace 'y' with '4x':
D = √[ (x - 51)² + (4x - 0)² ], or (after simplification)
D = √[ x² - 102x + 2601) + 16x² ], or  D = √[ 17x² - 102x + 2601 ].
This is the objective function in terms of one variable (x).
You don't specify the method to be used. Â The main method choices you have are (1) calculus and (2) algebra. Â
We want the x value at which this distance D is a minimum.  We can find that x value by finding the minimum of 17x² - 102x + 2601), whose graph is that of a parabola with minimum at x = -b/(2a).  Here, that x is x = 102/(34), or x = 3. Â
We conclude that the distance between the given point and the given line is a minimum when x = 3.
That distance is D = √[17x² - 102x + 2601], evaluated at x = 3:
√[ 17(9) - 102(3) + 2601 ] = 49.5 approximately
