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

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

Back

Use the section formula: If point P divides segment AB in the ratio m:n, then the coordinates of P are given by P(x,y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

What is the section formula used for?

Back

The section formula is used to find the coordinates of a point that divides a line segment into a specific ratio.

Front

If point P divides segment AB in the ratio 2:1, what does this mean?

Back

It means that the length of AP is twice the length of PB.

Front

What is the ratio of a directed line segment?

Back

The ratio of a directed line segment indicates how the segment is divided into parts, showing the relative lengths of the segments.

Front

How do you express a ratio?

Back

A ratio is expressed as 'a:b', where 'a' and 'b' are the quantities being compared.

Front

If point A is at -3 and point C is at 7, what point B divides AC in a 4:1 ratio?

Back

Point B is at 5.

Front

What is the significance of directed line segments in geometry?

Back

Directed line segments have a specific direction and are used to represent vectors and ratios in geometry.

Front

What does a ratio of 1:3 indicate in partitioning a segment?

Back

It indicates that the segment is divided into 4 equal parts, with one part on one side and three parts on the other.

Front

How can you determine the coordinates of a point that partitions a segment in a ratio of 3:1?

Back

Use the section formula with m=3 and n=1 to find the coordinates.