Distance and Midpoint

Front

What is the midpoint formula?

Back

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).

Front

Calculate the midpoint between (2, 3) and (4, 7).

Back

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

Front

What is the distance formula?

Back

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).

Front

Find the distance between (1, 2) and (4, 6).

Back

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

Front

What is the significance of the midpoint in geometry?

Back

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

Front

If the midpoint is (5, 5) and one endpoint is (3, 7), what is the other endpoint?

Back

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

Front

What is the perimeter of a rectangle with length 5 units and width 3 units?

Back

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

Front

How do you find the distance between two points on a coordinate plane?

Back

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

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

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

Front

What is the relationship between the endpoints and the midpoint?

Back

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