Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
(3,2) (7,8)

Answer 1

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.