Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. cordinates are 3,2 and 7,8
To find the length between the points (3,2) and (7,8), we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's consider the horizontal distance (d1) between the x-coordinates:
d1 = 7 - 3 = 4
Now, let's consider the vertical distance (d2) between the y-coordinates:
d2 = 8 - 2 = 6
Now we can apply the Pythagorean Theorem:
c² = d1² + d2²
c² = 4² + 6²
c² = 16 + 36
c² = 52
Taking the square root of both sides, we have:
c ≈ √52
c ≈ 7.21
Rounding to the nearest hundredth, the length between the points (3,2) and (7,8) is approximately 7.21 units.