Partitioning a Line Segment

Front

What is a directed line segment?

Back

A directed line segment is a line segment that has a specific direction from one endpoint to another, typically denoted as AB, where A is the starting point and B is the endpoint.

Front

What does it mean to partition a line segment?

Back

To partition a line segment means to divide it into smaller segments at a specific point, often in a given ratio.

Front

How do you find the coordinates of a point that partitions a line segment in a given ratio?

Back

Use the formula: P = (x1 + k*x2)/(1+k), (y1 + k*y2)/(1+k), where (x1, y1) and (x2, y2) are the coordinates of the endpoints and k is the ratio.

Tags

CCSS.HSG.GPE.B.6

Front

What is the ratio in the context of partitioning a line segment?

Back

The ratio indicates how the line segment is divided into parts. For example, a ratio of 1:3 means one part of the segment is compared to three parts of the segment.

Tags

CCSS.HSG.GPE.B.6

Front

If point P partitions line segment AB in a ratio of 1:3, how many total parts is the segment divided into?

Back

The segment is divided into 4 total parts (1 part + 3 parts).

Tags

CCSS.HSG.GPE.B.6

Front

Given points A(3, 5) and B(4, 3), find the coordinates of point P that partitions AB in a ratio of 3:1.

Back

P = (15/4, 7/2).

Tags

CCSS.HSG.GPE.B.6

Front

What is the formula for finding the coordinates of a point that divides a line segment in a ratio of m:n?

Back

P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Tags

CCSS.HSG.GPE.B.6

Front

If point P divides line segment AB in a ratio of 1:4, what is the relationship between the distances AP and PB?

Back

AP is 1 part and PB is 4 parts, meaning PB is four times longer than AP.

Tags

CCSS.HSG.GPE.B.6

Front

How do you determine the coordinates of point P that partitions JK at a ratio of 1:1?

Back

The coordinates of P will be the midpoint of J and K.

Tags

CCSS.HSG.GPE.B.6

Front

What is the significance of the ratio when partitioning a line segment?

Back

The ratio determines how the segment is divided and affects the position of the partition point.

Tags

CCSS.HSG.GPE.B.6