Segment Addition, Midpoint, and Distance

Front

What is the Segment Addition Postulate?

Back

The Segment Addition Postulate states that if point B is between points A and C, then AB + BC = AC.

Front

How do you find the distance between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the formula for finding the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Front

If the coordinates of point A are (3, 4) and point B are (7, 1), what is the distance AB?

Back

Distance AB = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Front

What does it mean for a point to be a midpoint?

Back

A midpoint divides a line segment into two equal parts.

Front

If DF = 9x - 39 and EF = 58, what is the value of x?

Back

Set 9x - 39 = 58, then solve for x: 9x = 97, x = 10.78.

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

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

Front

How do you determine if a point is the midpoint of a segment?

Back

Check if the distances from the midpoint to each endpoint are equal.

Front

What is the significance of the coordinates in the distance formula?

Back

The coordinates represent the positions of points in a Cartesian plane, which are used to calculate the distance between them.

Front

If the endpoints of a segment are (2, 3) and (10, 7), what is the midpoint?

Back

Midpoint = ((2 + 10)/2, (3 + 7)/2) = (6, 5).