Final answer:
To find the distance between points P1 and P2, apply the distance formula. Calculate the differences in x and y coordinates, square them, add together, and take the square root. The distance is approximately 2.48 units.
Step-by-step explanation:
To find the distance d(P1, P2) between the points P1 and P2, where P1 = (0.4, -0.4) and P2 = (2.3, 1.2), we use the distance formula derived from the Pythagorean theorem: d = √((x2 - x1)² + (y2 - y1)²).
Substituting the given values:
-
- x1 = 0.4, y1 = -0.4
-
- x2 = 2.3, y2 = 1.2
Now we calculate the differences:
-
- Δx = x2 - x1 = 2.3 - 0.4 = 1.9
-
- Δy = y2 - y1 = 1.2 - (-0.4) = 1.6
Squaring both differences and adding them, we get:
(Δx)² + (Δy)² = (1.9)² + (1.6)² = 3.61 + 2.56 = 6.17
Finally, taking the square root gives us the distance:
d = √6.17 ≈ 2.48 units