Question
Apply the Pythagorean Theorem to find the length between the two points (2,1 and 6,9). Round your answer to the nearest hundredth.
Answers
Answered by
GPT 3.5
To find the length between the two points (2,1) and (6,9), we can apply the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the points as A (2,1) and B(6,9). The distance between these two points forms the hypotenuse of a right-angled triangle.
We can find the length of the horizontal side by subtracting the x-coordinates: Δx = 6 - 2 = 4.
We can find the length of the vertical side by subtracting the y-coordinates: Δy = 9 - 1 = 8.
Using the Pythagorean Theorem, we can find the length between the points.
Hypotenuse² = Δx² + Δy²
Hypotenuse² = 4² + 8²
Hypotenuse² = 16 + 64
Hypotenuse² = 80
To find the length of the hypotenuse (the distance between the two points), we take the square root of both sides:
Hypotenuse = √80 ≈ 8.94
Rounded to the nearest hundredth, the length between the two points (2,1) and (6,9) is approximately 8.94.
Let's label the points as A (2,1) and B(6,9). The distance between these two points forms the hypotenuse of a right-angled triangle.
We can find the length of the horizontal side by subtracting the x-coordinates: Δx = 6 - 2 = 4.
We can find the length of the vertical side by subtracting the y-coordinates: Δy = 9 - 1 = 8.
Using the Pythagorean Theorem, we can find the length between the points.
Hypotenuse² = Δx² + Δy²
Hypotenuse² = 4² + 8²
Hypotenuse² = 16 + 64
Hypotenuse² = 80
To find the length of the hypotenuse (the distance between the two points), we take the square root of both sides:
Hypotenuse = √80 ≈ 8.94
Rounded to the nearest hundredth, the length between the two points (2,1) and (6,9) is approximately 8.94.