Line Segment Partition

Front

What is a line segment?

Back

A line segment is a part of a line that is bounded by two distinct endpoints.

Front

Define partitioning a line segment.

Back

Partitioning a line segment involves dividing it into smaller segments based on a specific ratio.

Front

What does the ratio AP:PB = 1:4 indicate?

Back

It indicates that the length of segment AP is one-fourth the length of segment PB.

Front

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

Back

Use the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m:n is the ratio.

Front

What is the section formula?

Back

The section formula is used to find the coordinates of a point dividing a line segment in a given ratio.

Front

If A is at (-5, 8) and B is at (9, 3), how do you find P that divides AB in the ratio 2:7?

Back

Use the section formula: P = ((2*9 + 7*(-5))/(2+7), (2*3 + 7*8)/(2+7)) = (-1, 46/7).

Front

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

Back

The ratio determines how the lengths of the segments compare to each other.

Front

What does it mean to partition a line segment in the ratio 1:1?

Back

It means that the two segments created by the partitioning point are equal in length.

Front

How can you express the relationship of segments in a directed line segment?

Back

By using ratios to compare the lengths of the segments created by the partitioning point.

Front

What is the result of partitioning a line segment into three equal parts?

Back

Each part will have the same length, and the ratio of the segments will be 1:1:1.