Question

geometry concepts and connections unit 6 georgias k - 12 mathematics standards
name:
date:
tangents intersecting a radius
diagnostic assessment
line l represents a straight part of the shoreline at a beach. suppose you are in the ocean at point c and you want to get to the shore as fast as possible. assume there is no current. segments cj and cd represent 2 possible paths.
diego says, no matter where we put point d, the pythagorean theorem tells us that segment cj is shorter than segment cd. so, segment cj represents the shortest path to shore.
do you agree with diego? explain your reasoning.

Explanation:

The shortest distance from a point to a line is the perpendicular distance. Let the perpendicular from point C to line $\ell$ be $CJ$. For any other point D on $\ell$, triangle $CJD$ is a right - triangle with hypotenuse $CD$. By the Pythagorean theorem, $CD^{2}=CJ^{2}+JD^{2}$, so $CD > CJ$.

Answer:

Yes, I agree with Diego. The perpendicular segment $CJ$ from point C to the line $\ell$ (shoreline) is the shortest distance as per the Pythagorean theorem for any right - triangle formed with $CJ$ and another path $CD$ to a non - perpendicular point D on the line.