Question

Two points are located at (-3,-8) and (2,0). How can you use the Pythagorean theorem to find the distance between these two points? On a coordinate plane, a triangle has points (-3,-8), (2,0), and (2,-8).

Answer 1

Step-by-step explanation:

by seeing the line between the 2 points as Hypotenuse of a right-angled triangle, where one leg is the horizontal x-coordinate difference, and the second leg is the vertical y-coordinate difference.

so, in our case

distance² = (-3 - 2)² + (-8 - 0)² = 25 + 64 = 89

distance = sqrt(89) = 9.433981132...

Answer 2

Using the Pythagorean theorem, the distance between the points (-3,-8) and (2,0) is calculated by finding the lengths of the triangle's legs (5 and 8 units) and solving for the hypotenuse, which is approximately 9.434 units.

Step-by-step explanation:

To find the distance between the two points (-3,-8) and (2,0) using the Pythagorean theorem, we first consider the triangle formed by these points and the point (2,-8). The horizontal leg of the triangle is the difference in the x-values of the points (-3 and 2), which is 5 units. The vertical leg is the difference in the y-values of the points (-8 and 0), which is 8 units.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². To compute the straight-line distance, which is the length of the hypotenuse, we square each of the legs, sum them, and then take the square root.

The calculations are as follows:

• a² = 5² = 25
• b² = 8² = 64
• c² = a² + b² = 25 + 64 = 89
• c = √(89) ≈ 9.434

Therefore, the distance between the points (-3,-8) and (2,0) is approximately 9.434 units.