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.

Tags

CCSS.HSG.GPE.B.6

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).

Tags

CCSS.HSG.GPE.B.6

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.

Tags

CCSS.HSG.GPE.B.6

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).

Tags

CCSS.HSG.GPE.B.7

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.

Tags

CCSS.HSG.CO.A.1

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).

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.GPE.B.6

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.

Tags

CCSS.4.MD.A.2

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.

Tags

CCSS.HSG.SRT.B.4

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.

Tags

CCSS.6.G.A.3