U6L15 Weighted Averages

What is the midpoint of the segment connecting (1,2) and (5,2)?

What is the midpoint of the segment connecting (5,2) and (5,10)?

What is the midpoint of the segment connecting (1,2) and (5,10)?

Which point partitions AB in a 1 : 2 ratio?

In other words, if we call that point C, which point makes the ratio AC : CB = 1 : 2?

Which point partitions AB in a 2 : 1 ratio?

Consider just the horizontal part (the blue line) from A to B. How long is it?

So the total horizontal distance is 6 units.

If we go only 2/3 of that distance, how many units do we go?

The distance from 2 to 8 was 6 because 6 = 8-2.

If we didn't know where A and B are...

The distance from A to B is C because C =

We wanted to go 2/3 of 6 units, so we got 4 by calculating 2/3(6)=4.

If the distance from A to B is "B-A", write an expression that says we only want to go 2/3 of that distance.

So now we know that we can add 2/3(B-A) to our starting point to get our ending point.

If we want to travel from A to B, where is our starting point?

Write an expression for the point that partitions A and B in a 1 : 4 ratio.

Find the point that partitions AB in a 1:4 ratio. Label it B'.

Find the point that partitions AD in a 1:4 ratio. Label it D'.

Find the point that partitions AC in a 1:4 ratio. Label it C'.

AB'C'D' is a dilation of ABCD from center A by scale factor