Math DEF Coordinates Find E?

[MominPervaiz]

I received a homework Geometry break packet and there is a question I have never learned. The problem is, "The endpoints of DEF are D(11,4) and F(16,14). Determine and state the coordinates of point E, if DE:EF = 2:3."
The answer to the problem is given.

2/5 ⋅(16 − 1) = 6 2/5 ⋅(14 − 4) = 4 (1 + 6,4 + 4) = (7,8)

I still do not understand the question and how to solve it. Why was 2:3, had 2 divided by 5? Is there any formula for this? Please help me.

 

[Deleted member 4993]

I received a homework Geometry break packet and there is a question I have never learned. The problem is, "The endpoints of DEF are D(11,4) and F(16,14). Determine and state the coordinates of point E, if DE:EF = 2:3."
The answer to the problem is given.

2/5 ⋅(16 − 1) = 6 2/5 ⋅(14 − 4) = 4 (1 + 6,4 + 4) = (7,8)

I still do not understand the question and how to solve it. Why was 2:3, had 2 divided by 5? Is there any formula for this? Please help me.

If we assume DE = 2 inch, and DE:EF = 2:3 → How long is EF? → How long is (DE + EF =) DF?

 

[starTman08]

I received a homework Geometry break packet and there is a question I have never learned. The problem is, "The endpoints of DEF are D(11,4) and F(16,14). Determine and state the coordinates of point E, if DE:EF = 2:3."
The answer to the problem is given.

2/5 ⋅(16 − 1) = 6 2/5 ⋅(14 − 4) = 4 (1 + 6,4 + 4) = (7,8)

I still do not understand the question and how to solve it. Why was 2:3, had 2 divided by 5? Is there any formula for this? Please help me.

[I'm not sure, just scan my idea]

1/ I don't think the answer is right - if E (7,8) - we can check the length DE/EF - distance between two points.

2/ If DEF is a line - find the formula y = ax + b - we have enough information(2 points) - let E (x, y) - so E will be (x, something with x) - depend on DE/EF = 2/3 with only x.

 

[stapel]

1/ I don't think the answer is right - if E (7,8) - we can check the length DE/EF - distance between two points.

Okay; what distances did you get?

 

[pka]

I received a homework Geometry break packet and there is a question I have never learned. The problem is, "The endpoints of DEF are D(11,4) and F(16,14). Determine and state the coordinates of point E, if DE:EF = 2:3."
The answer to the problem is given.

2/5 ⋅(16 − 1) = 6 2/5 ⋅(14 − 4) = 4 (1 + 6,4 + 4) = (7,8)

That is incorrect! The correct answer is \(\displaystyle E=\left(\frac{63}{5},8\right)\), the point must be between D & F.

\(\displaystyle \overline{DF}=\{(11+4t,4+10t):0\le t\le 1\}\) you want \(\displaystyle t=\frac{2}{5}\).

 

[Haymedoots]

The correct answer is 13,8

 

[Haymedoots]

Edit that a bit:

The correct answer is 11+2/5(16-11), 4+2/5(14-4) which is 13,8