Apply the pythagorean theorem to find the length between (0,4) and (-3,0)
To apply the Pythagorean theorem, we need to find the lengths of the two legs of the right triangle formed by the given points.
Let's call the first point (0, 4) as point A and the second point (-3, 0) as point B.
The horizontal leg is the difference in x-coordinates, which is:
Length of leg AB = x-coordinate of point B - x-coordinate of point A = -3 - 0 = -3
The vertical leg is the difference in y-coordinates, which is:
Length of leg AC = y-coordinate of point B - y-coordinate of point A = 0 - 4 = -4
Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying the Pythagorean theorem, we have:
Length of hypotenuse (BC)² = Length of leg AB² + Length of leg AC²
BC² = (-3)² + (-4)²
BC² = 9 + 16
BC² = 25
Taking the square root of both sides, we get:
BC = √25
BC = 5
Therefore, the length between (0, 4) and (-3, 0) is 5 units.