Question

(06.04 MC)
A point T on a segment with endpoints D(1, 4) and F(7, 1) partitions the segment in a 2:1 ratio. Find T. must show all work to receive credit.

Answer 1

sketch of the points

Answer 2

because the ratio is 2:1, we can think of DT being 2x units and TF being x units, so that DT/TF = 2.

the whole length is 3x, so DT is 2/3 of the whole length and TF is 1/3 of the whole length

Answer 3

this same rule applies to the horizontal and vertical distances

Answer 4

on our triangle, let's call the bottom right corner point A. it has the same x-coordinate as D and the same y-coordinate as F, so the point is (1,1)

Answer 5

*bottom left corner sorry

now, to find T, find:
- the x-coordinate that is 2/3 of the way between A and F
and
- the y-coordinate that is 2/3 of the way between D and A

let me know if you're still stuck or if anything was unclear

Answer 6

can u just solve it for me please

Answer 7

@aarondkdkjd solving it for you is against the rules. You were given an explantion on how to do it so please work towards that c: