Partition Line Segments

Front

What is a partition of a line segment?

Back

A partition of a line segment divides it into two or more parts based on a specified ratio.

Front

If a line segment is divided in the ratio 3:1, how many total parts are there?

Back

4 parts.

Front

True or False: A directed line segment MN partitioned into a ratio of 1:2 is the same as NM partitioned into a ratio of 2:1.

Back

True.

Front

How do you find a point P that divides a line segment AB 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 in coordinate geometry?

Back

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

Front

Find P, so that AP is two-sevenths of PB. A is at (-5, 8) and B is at (9, 3). What is P?

Back

P = (-1, 46/7).

Front

Find P, so that AP is three-elevenths of PB. Given A (-6, -6) and B(-2, 1). What is P?

Back

P = (-54/11, -45/11).

Front

If point A is at (-5, 8) and point B is at (9, 3), what is the ratio of AP to PB if P is at (-1, 6.6)?

Back

The ratio is 2:5.

Front

What does it mean to partition a line segment in the ratio 2:5?

Back

It means that the segment is divided into 7 equal parts, where 2 parts are assigned to AP and 5 parts to PB.

Front

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

Back

Use the formula: P = ((x1*m + x2*n)/(m+n), (y1*m + y2*n)/(m+n)).