Dividing a line segment into three parts ( formula/steps).

[Oxymoron]

Given A( -1,3 ) and B( 4,5 ) determine the coordinates of the points that divide the line segment into three congruent parts.

 

[stapel]

Given A( -1,3 ) and B( 4,5 ) determine the coordinates of the points that divide the line segment into three congruent parts.

What is the difference in the x-values? What is one-third of this value? Starting at x = -1, what should be the four x-values (the given beginning value, the given end value, and the two values in between)?

What is the difference in the y-values? What is one-third of this value? Starting at y = 3, what should be the four y-values?

You are given the first and last points. From the above, what should be the second and third points?

If you get stuck, please reply showing all of your work and reasoning. Thank you!

Eliz.

 

[tkhunny]

There are fancy formulas for that, but I prefer just to note the weighted average. It's a generalization of the mid-point formula.

1/3 from A to B is simple (2/3)A + (1/3)B

2/3 from A to B is simple (1/3)A + (2/3)B

Notice how the ratio that is wanted is on the ending point.