The Pythagorean Theorem is used to calculate the distance between two points in a Cartesian coordinate system. Let's denote the two points as P1(x1, y1) and P2(x2, y2).
P1 = (6, 9)
P2 = (2, 1)
To use the Pythagorean Theorem to find the distance (d) between these two points, we will calculate the differences in the x-coordinates (Δx) and y-coordinates (Δy), and then apply the theorem:
Δx = x2 - x1 = 2 - 6 = -4
Δy = y2 - y1 = 1 - 9 = -8
Next, we square those differences and sum them up:
Δx² = (-4)² = 16
Δy² = (-8)² = 64
Summing these we get:
Δx² + Δy² = 16 + 64 = 80
Now we take the square root of that sum to find the distance:
d = √(Δx² + Δy²)
d = √80
d ≈ 8.94
Rounding to the nearest hundredth, the distance between the two points is approximately 8.94 units.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
(6,9)
(2,1)
1 answer
1 answer