Distance and Midpoint

The midpoint formula is used to find the midpoint (M) between two points (x1, y1) and (x2, y2): M = ((x1 + x2)/2, (y1 + y2)/2).

Midpoint = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

The distance formula is used to find the distance (d) between two points (x1, y1) and (x2, y2): d = √((x2 - x1)² + (y2 - y1)²).

Distance = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

The midpoint divides a line segment into two equal parts and is often used in constructions and proofs.

Let the other endpoint be (x, y). Using the midpoint formula: (5, 5) = ((3 + x)/2, (7 + y)/2). Solving gives (7, 3).

Perimeter = 2(length + width) = 2(5 + 3) = 16 units.

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Distance = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

The midpoint is the average of the coordinates of the endpoints.