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 partition a directed line segment in a given ratio?

Back

To partition a directed line segment in a ratio of m:n, you divide the segment into m+n equal parts and take m parts from the starting point to find the partition point.

Front

If a directed line segment AB is partitioned in the ratio 1:2, what does this mean?

Back

It means that the distance from A to the partition point P is one part, and the distance from P to B is two parts, making the total distance divided into three equal segments.

Front

Is the statement 'Directed line segment MN partitioned into a ratio of 1:2 is the same as directed line segment NM partitioned into a ratio of 1:2' true or false?

Back

False. The direction matters in directed line segments.

Front

Given points W(3,7) and Y(13,-8), how do you find the coordinates of point X that partitions WY in the ratio 3:2?

Back

Use the section formula: X = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)), where m=3, n=2, (x1,y1) = W, (x2,y2) = Y.

Front

What are the coordinates of point P that partitions line segment AB with A(-9,-7) and B(3,8) in the ratio 2:1?

Back

P = \left( \frac{2(3) + 1(-9)}{2+1}, \frac{2(8) + 1(-7)}{2+1} \right) = (-1, 3).

Front

How do you find the coordinates of point P that partitions line segment AB with A(8, -4) and B(-6, -11) in the ratio 2:7?

Back

Use the section formula: P = \left( \frac{2(-6) + 7(8)}{2+7}, \frac{2(-11) + 7(-4)}{2+7} \right) = (4, -6).

Front

What is the section formula used for finding the coordinates of a point that divides a line segment in a given ratio?

Back

The section formula states that if a point P divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of P are given by: P = \left( \frac{mx2 + nx1}{m+n}, \frac{my2 + ny1}{m+n} \right).

Front

If point C divides the directed line segment from A(-3, -1) to B(5, 7) in the ratio 1:3, how do you find the coordinates of C?

Back

Use the section formula: C = \left( \frac{1(5) + 3(-3)}{1+3}, \frac{1(7) + 3(-1)}{1+3} \right) = (-1, 1).

Front

What is the significance of the order of points in a directed line segment?

Back

The order of points in a directed line segment determines the direction of the segment and affects the ratios used for partitioning.