Sure, let's tackle this in two parts. First, we'll find the distance between the two points. Second, we'll calculate the midpoint.
1. To find the distance, we'll use the Euclidean distance formula, which is √[(x₂ - x₁)² + (y₂ - y₁)²] for two points (x₁, y₁) and (x₂, y₂).
Here, our points are (-7, 21) and (12, -9). Thus, x₁ = -7, y₁ = 21, x₂ = 12, and y₂ = -9.
Substituting these into the distance formula, we get:
Distance = √[(12-(-7))² + ((-9)-21)²] = √[361+900] = √[1261] ≈ 35.51.
So the distance between the points is approximately 35.51 units.
2. The midpoint is calculated using the formula [(x₁+x₂)/2 , (y₁+y₂)/2]. Substituting our values in, we get:
Midpoint = [(-7+12)/2 , (21+(-9))/2] = [5/2, 12/2] = (2.5,6)
So the midpoint between the points (-7,21) and (12,-9) is (2.5, 6).