Partition Line Segments Learning Target Students can find

Partition Line Segments Learning Target: Students can find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Bell work 9/5/2017 Calculate the distance and the midpoint. 1. (2, -3) and (10, -5)

What is partition line? Partitioning AB into a 2: 3 ratio implies starting at point A. The ratio of 2: 3 indicates that the segment will actually be divided into 5 equal sections. If P is the partition point, it will be located 2 of the equal sections away from A and 3 of the equal sections away from B. Consequently, P will be closer to A than it will be to B, since A is the initial point.

Partitions

What do you do when it doesn’t partition evenly?

Partitioning using a Formula The scale factor of the dilation, k, is equal to the ratio of AP to the total length AB.

Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 2.

A(3, 4), B(6, 10); 3 to 2. To find the coordinates of point P… 3 6

Example 1: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(1, 3), B(8, 4); 4 to 1.

Example 2: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, 1), B(4, 5); 3 to 7.

Example 3: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(8, 0), B(3, -2); 1 to 4.

Example 4: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2.