Question

Can someone explain to me how this person set up this trigonometry equation?

Answer 1

well usign the ratios
DT/TF=2/1


or DT = 2DF

so to find t
xt=1+2×7/2+1 yt=4+2×1/1+2


just finish the calculation to find T

Answer 2

can you post the entire question?

Answer 3

heres the question: @baru

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.

Answer 4

okay i see you set up the segment in the first graph, but what did you do in the second? just make the right triangle, right?

Answer 5

yes

Answer 6

okay, whats next

Answer 7

ok
the question tells us that DT:TF = 2:1
or DT/TF=2

i hope you remember you similar triangles,
because from the triangle i have drawn, we can say DT/TF = AB/BF

making sense?

Answer 8

a little, but the person who made that equation said that he used DT/TF=2/1 or DT=2DF. How did he get that equation?

Answer 9

that information is given,

the question says T splits DF in the ration 2:1

in other words DT:TF=2:1

which is the same as
\(\frac{DT}{TF}=\frac{2}{1}\)

Answer 10

oh okay, i see. how did he set up the next equations?

Answer 11

from similar triangles we have
DT/TF = AB/BF

or AB/BF=2

ok?

Answer 12

yeah

Answer 13

let the point B have x co-ordinate \(x_t\)

can you find the length of AB and BF in terms of \(x_t\) ?