Question

Will Medal First Answer!

Douglas has a segment with endpoints I(5, 2) and J(9, 10) that is divided by a point K such that IK and KJ form a 2:3 ratio. He knows that the distance between the x-coordinates is 4 units. Which of the following fractions will let him find the x-coordinate for point K?

2/3

2/5

3/2

3/5

Answer 1

\(\frac{\text{IK}}{\text{KJ}} = 2/3\)
\( \rightarrow \text{IK} = \frac23 KJ\). (*)

Use (*) and
\(\text{IK} + \text{KJ} = \text{distance(I, J)} = \sqrt{8^2 + 4^2} = \sqrt{64+16}\)
to compute \(\text{KJ}\).

Answer 2

Other way: divide \(\text{IJ}\) in 5 segments of same lengths. \(\text{IK}\) is the union of the two first segments.

Answer 3

so 2/5?

Answer 4

I don't understand that part of the statement :
"He knows that the distance between the x-coordinates is 4 units. Which of the following fractions will let him find the x-coordinate for point K?
2/3
2/5
3/2
3/5"

Answer 5

i think it means the distance between the ordered pairs x coordinate

Answer 6

Well, actually, by Thalès' theorem,...
it will be a \(\frac25\times 4\) distance between the x-coordinates of I and K...

Answer 7

I don't find the statement very clear, but now I think the answer is 2/5.

Answer 8

ok, i think the answer is 3/5. I keep asking getting varied answers
i think i will ask my teacher