Partition Line Segments (2 Dimensions)

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Presentation transcript:

Partition Line Segments (2 Dimensions) Learning Target: Students can find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Partition – 2 Dimensional 1. Add the ratio: 2:1 = 2+1 = 3 = r 2. Find the distance between the x’s: B – A = d 3. Divide the distance by ratio: d/r = interval 4. Draw number line 5. Draw Lines at interval 6. Shade by first number in the ratio 7. Repeat for the y’s

Partitioning Line Segments in 2 Dimensions with Task Worksheet – Practice Partitioning Line Segments in 2 Dimensions with Task

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

Formula

Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 2. In order to divide the segment in the ratio of 3 to 2, think of dividing the segment into 3 + 2 or 5 congruent pieces.

A(3, 4), B(6, 10); 3 to 2. 3 AB has a rise of 6. 6 AB has a run of 3.

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

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.

Homework Worksheet

Partitioning Line Segments in 2 Dimensions HW Partitioning Line Segments in 2 Dimensions