To calculate the distance between two points in a coordinate plane, you have to follow these steps:
Step 1: Identify the points' coordinates. In this case, we have point F which coordinates are (-1,6) and point K with coordinates (4,-2).
Step 2: Calculate the horizontal and vertical differences between points. The formula is simple subtraction:
- Horizontal difference = x2 - x1
- Vertical difference = y2 - y1
Substituting the coordinates of points F and K, you get:
Horizontal difference = 4 - (-1) = 5
Vertical difference = -2 - 6 = -8
Step 3: Apply the Pythagorean theorem to calculate the distance between these two points. The theorem formula is:
Distance = √((horizontal difference)² + (vertical difference)²)
Substituting the previously calculated differences, you get:
Distance = √((5)² + (-8)²) = √(25 + 64) = √89 ≈ 9.44 units
So, the distance between point F and K is approximately 9.44 units.