Apply the Pythagorean Theorem to find the length between (2,7) and (−2, 0) .
To apply the Pythagorean theorem to find the length between two points, we need to find the distance between their x-coordinates and the distance between their y-coordinates.
The distance between the x-coordinates is given by:
Δx = x₂ - x₁ = (-2) - 2 = -4
The distance between the y-coordinates is given by:
Δy = y₂ - y₁ = 0 - 7 = -7
Now, we can use these values to find the length between the two points:
d = √(Δx² + Δy²)
d = √((-4)² + (-7)²)
d = √(16 + 49)
d = √65
So, the length between (2,7) and (-2,0) is √65 units.