Question

A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio. Find Q. You must show all work to receive credit.

Answer 1

In order to divide AC into a 4:1 ratio, you need to split the line at the 4/5 mark (that way, the left segment is 4/5 of the whole, the right segment is 1/5 of the whole, and thus left:right = 4/1)

to do this, you'll need to find the 4/5 point between the x-coordinates, as well as the y-coordinates.

I'll show you how to do the x-coordinates first, then you can do the y-coordinates.

x-coordinates: 2 and 4. 4-2 = 2, so the x-coordinates are 2 units apart.

4/5 of 2 units ---> (4/5)(2) = 8/5 or 1.6

add this onto the lower x-coordinate (2) to get 2 + 1.6 = 3.6. which is the x-coordinate of point Q.

repeat with the y-coordinates.

Answer 2

Thank you so much. I finally understand.