7.3 Partitioning a Segment

Front

What is the definition of partitioning a segment?

Back

Partitioning a segment refers to dividing a line segment into smaller segments in a specific ratio.

Front

If a segment is divided in the ratio 4:1, how many total parts are there?

Back

5 parts.

Front

What does the ratio 3:1 indicate when partitioning a segment?

Back

It indicates that the segment is divided into 4 parts, with one part being three times longer than the other.

Front

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

Back

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

Front

Given points A(-1,2) and B(7,14), what is the point P that partitions AB in a ratio of 1:3?

Back

P is (1,5).

Front

What is the section formula used for partitioning a segment?

Back

The section formula is P(x,y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

If point P divides segment AB in the ratio 1:2, what is the relationship of the lengths AP and PB?

Back

AP is one part and PB is two parts.

Front

What is the significance of directed line segments in partitioning?

Back

Directed line segments have a specific direction, which affects the ratios when partitioning.

Front

How do you express a ratio in simplest form?

Back

Divide both terms of the ratio by their greatest common divisor.

Front

What is the ratio of a segment if point P divides it into two equal parts?

Back

The ratio is 1:1.