A point T on a segment with endpoints F (1,8) and G (4,1) partitons the segment in a 3:2 ratio. Find T.

Question

Express your answer as an integer or simplified fraction SHOW ALL WORK!!!

T (___, ___)

Answer 1

If you sketch it out you'll see the problem looks like this:

I noted the lengths of the line segment as 3x and 2x because we don't know the exact lengths but they have a ratio of 3:2. Notice that the ratio of FT to FG is actually 3/5. That means we can find the x-coordinate of point T by going 3/5 from F to G in the x-direction:

Distance in the x-direction from F to G is 4 - 1 or 3. To go 3/5 of 3 we can multiply 3/5 • 3/1 = 9/5 = 1.8 So we need to go 1.8 in the x-direction from point F to get to point T. That means the x-coordinate of point T is 1 + 1.8 = 2.8

Distance in the y-direction from F to G is 1 - 8 or -7. To go 3/5 of -7 we can multiply 3/5 • (-7/1) = -21/5 = -4.2 So we need to go -4,2 in the y-direction from point F to get to point T. That means the y-coordinate of point T is 8 - 4.2 = 3.8

So Point T has coordinates (2.8, 3.8)

Answer 2

1 + 3/5 x 3 = 1+9/5 = 14/5 = 2.8 = x

8- 3/5 x 7 = 8 -21/5 = 40/5-21/5 = 19/5 = 3.8 = y

T [x,y] = [2.8, 3.8] = [14/5, 19/5] = [2 4/5, 3 4/5]