Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

The coordinate points are 5
4
3
2
1
0
-5 -4 -3 -2 -1 -0 1 2 3 4 5 -1
-2
-3
-4
-5

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To apply the Pythagorean theorem to find the length between two points in a Cartesian coordinate system, you first need to have two specific points provided in the form of (x1, y1) and (x2, y2).

From your message, it looks like the coordinate points are not clearly defined; you've given a visual of the coordinate system axis numbers from -5 to 5 on both the x-axis (horizontal) and y-axis (vertical). However, there are no specific points given for which you want to find the distance between.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This is written as:

c² = a² + b²

This theorem can be rearranged to solve for c:

c = √(a² + b²)

In a two-dimensional Cartesian coordinate system, the difference in the x-coordinates (Δx = x2 - x1) would represent one side of the triangle (a), and the difference in the y-coordinates (Δy = y2 - y1) would represent the other side (b). The length of the hypotenuse of this right triangle, representing the distance between the two points (d), would be:

d = √((x2 - x1)² + (y2 - y1)²)

Please provide the specific coordinates of the two points you would like the distance computed between, and I can use this formula to find the length for you. Without concrete points, the length cannot be calculated.