apply the Pythagorean theorem to find the distance between (2, 4) and (-2, -1) round to the nearest hundredth
To find the distance between the points (2, 4) and (-2, -1) using the Pythagorean theorem, we need to calculate the length of the hypotenuse of the right triangle formed by connecting these two points.
The Pythagorean theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) of the right triangle.
Using the given points, we can find the lengths of the two sides:
a = x₂ - x₁ = -2 - 2 = -4
b = y₂ - y₁ = -1 - 4 = -5
Now we can apply the Pythagorean theorem:
c² = a² + b²
c² = (-4)² + (-5)²
c² = 16 + 25
c² = 41
To find the length of c, we take the square root of both sides:
c = √41 ≈ 6.40 (rounded to the nearest hundredth)
Therefore, rounding to the nearest hundredth, the distance between (2, 4) and (-2, -1) is approximately 6.40.