3.5 Partitioning Directed Line Segement

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

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

Back

To find the coordinates of a point P that partitions a directed line segment AB in the ratio m:n, use the formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)), where A(x1, y1) and B(x2, y2).

Front

If the ratio is 3:1, how many total parts are there?

Back

There are 4 total parts (3 + 1 = 4).

Front

Given points A(-2, 4) and B(7, -2), find the coordinates of point P that divides AB in the ratio 1:2.

Back

The coordinates of point P are (1, 2).

Front

Given points A(-1, 2) and B(7, 14), find the coordinates of point P that divides AB in the ratio 1:3.

Back

The coordinates of point P are (1, 5).

Front

What is the partition fraction if AP:PB is 2:3?

Back

The partition fraction is 2/5.

Front

Given line segment WY with W(3, 7) and Y(13, -8), if point X partitions WY such that WX:XY is 3:2, find the coordinates of X.

Back

The coordinates of X are (9, 9).

Front

What is the formula for finding the ratio of two segments on a line?

Back

The ratio of two segments AB and BC can be expressed as AB:BC = length of AB:length of BC.

Front

How do you express a ratio in fractional form?

Back

A ratio of m:n can be expressed in fractional form as m/(m+n).

Front

What does it mean to partition a line segment?

Back

To partition a line segment means to divide it into parts that are proportional to a given ratio.