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.
Is a dilation of ? Justify your answer.