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IM Geo.6.15 Lesson: Weighted Averages

For the questions in this activity, use the coordinate grid if it is helpful to you.

What is the midpoint of the segment connecting  and ?

What is the midpoint of the segment connecting  and ?

What is the midpoint of the segment connecting  and ?

Point A has coordinates (2,4). Point B has coordinates (8,1).

Find the point that partitions segment  in a  ratio.

Calculate .

What do you notice about your answers to the first 2 questions?

For 2 new points  and , write an expression for the point that partitions segment  in a  ratio.

Consider the general quadrilateral  with , , , and . Find the midpoints of each side of this quadrilateral.

Show that if these midpoints are connected consecutively, the new quadrilateral formed is a parallelogram.

Here is quadrilateral ABCD.

  • Find the point that partitions segment  in a  ratio. Label it .
  • Find the point that partitions segment  in a  ratio. Label it .
  • Find the point that partitions segment  in a  ratio. Label it .
Is  a dilation of ? Justify your answer.