Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
(3,2) (7,8)
To find the distance between two points, you can use the Pythagorean Theorem by treating the distance between these points as the hypotenuse of a right-angled triangle. The difference in x-coordinates and y-coordinates of the points will be the lengths of the other two sides of the triangle.
Given the two points (3,2) and (7,8), you can calculate the differences in the x and y coordinates:
Δx = x2 - x1 = 7 - 3 = 4
Δy = y2 - y1 = 8 - 2 = 6
Now you have the lengths of the two sides of the triangle, and you can apply the Pythagorean Theorem:
c² = a² + b²
where c is the hypotenuse, and a and b are the other two sides of the triangle.
Thus:
distance² = Δx² + Δy²
distance² = 4² + 6²
distance² = 16 + 36
distance² = 52
Now, take the square root of both sides to find the distance:
distance = √(52)
distance ≈ 7.2111
Rounding this to the nearest hundredth gives:
distance ≈ 7.21
The length between the two points is approximately 7.21 units.