Segment Bisector, Midpoint, Distance

Front

What is a midpoint in geometry?

Back

A midpoint is a point that divides a line segment into two equal parts.

Front

How do you find the coordinates of the midpoint M of a line segment AB with endpoints A(x1, y1) and B(x2, y2)?

Back

The coordinates of the midpoint M are given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

If M is the midpoint of segment AB, and AM = 5x + 10 and MB = 4x + 16, how do you find the value of x?

Back

Set AM equal to MB, then solve for x: 5x + 10 = 4x + 16.

Front

What is the distance formula used to calculate the distance between two points A(x1, y1) and B(x2, y2)?

Back

The distance d is given by d = √((x2 - x1)² + (y2 - y1)²).

Front

What does it mean for a line to be a segment bisector?

Back

A segment bisector is a line, ray, or segment that divides another segment into two equal parts.

Front

If AM = 4n - 40 and MB = 7(-2n + 2), how do you find the value of n when M is the midpoint?

Back

Set AM equal to MB, then solve for n: 4n - 40 = 7(-2n + 2).

Front

What is the relationship between the lengths of segments when a point is the midpoint?

Back

The lengths of the segments on either side of the midpoint are equal.

Front

How can you express the length of a segment in terms of a variable?

Back

You can express the length of a segment as an algebraic expression, such as AB = 2x + 3.

Front

If AB = 2x + 3, BC = 3x - 5, and AC = 38, how do you find the value of x?

Back

Set up the equation AB + BC = AC, then solve for x: (2x + 3) + (3x - 5) = 38.

Front

What is the significance of the distance between two points in geometry?

Back

The distance between two points represents the length of the shortest path connecting them.