Midpoint and distance formula

Front

What is the Midpoint Formula?

Back

The Midpoint Formula is used to find the midpoint (M) of a line segment connecting two points (x1, y1) and (x2, y2). It is given by: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

How do you find the y-coordinate of the midpoint?

Back

To find the y-coordinate of the midpoint, use the formula: (y1 + y2)/2, where y1 and y2 are the y-coordinates of the endpoints.

Front

What is the Distance Formula?

Back

The Distance Formula is used to calculate the distance (d) between two points (x1, y1) and (x2, y2). It is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

Find the midpoint of the points (2, 3) and (4, 5).

Back

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

Front

Find the distance between the points (1, 1) and (4, 5).

Back

Distance = √((4 - 1)² + (5 - 1)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the significance of the Midpoint Formula in geometry?

Back

The Midpoint Formula helps in finding the center point of a line segment, which is essential in various geometric constructions and proofs.

Front

If the points are (x1, y1) and (x2, y2), how do you find the x-coordinate of the midpoint?

Back

The x-coordinate of the midpoint is found using the formula: (x1 + x2)/2.

Front

What is the geometric interpretation of the Distance Formula?

Back

The Distance Formula calculates the straight-line distance between two points in a coordinate plane, representing the length of the line segment connecting them.

Front

Find the y-coordinate of the midpoint of the line segment connecting (2, 1) and (4, 3).

Back

Y-coordinate = (1 + 3)/2 = 2.

Front

What is the relationship between the coordinates of the endpoints and the midpoint?

Back

The coordinates of the midpoint are the averages of the corresponding coordinates of the endpoints.