Question

The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to the shoreline. Write an equation that represents this path.

Answer 1

Answer:

Step-by-step explanation:

To define the perpendicular line we need to first know the slope of the reference line graphed.

m=(y2-y1)/(x2-x1) we have points (0,5) and (2,1)

m=(1-5)/(2-0)

m=-4/2

m=-2

For lines to be perpendicular their slopes must satisfy

m1m2=-1, we have a line with a slope of -2 so

-2m=-1

m=1/2, so our perpendicular line is so far

y=x/2+b, it must have point (3,2) so we can solve for b

2=3/2+b

b=1/2, so the swimmer will travel along the line

y=x/2+1/2