options: Explain a proof of the Pythagorean Theorem and its converse.

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
problem_activity: Task
Plot the points (5,3), (-1,1), and (2,-3) in the coordinate plane and find the lengths of the three segments connecting the points.
Find the distance between (5,9) and (-4,2) without plotting the points.
If $(u,v)$ and $(s,t)$ are two distinct points in the plane, what is the distance between them? Explain how you know.
Does your answer to (c) agree with your calculations in parts (a) and (b)? Explain.


correct_option_index: 1