Question

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. You must show all work to receive credit.

Answer 1

@hartnn

Answer 2

@FutureMathProfessor @whpalmer4 @ganeshie8 @thomaster @RadEn

Answer 3

@SolomonZelman

Answer 4

I assume there are 2 values for T..

Answer 5

(3,3) and (5.2) are the answers

Answer 6

so thats it

Answer 7

hey you there @FutureMathProfessor

Answer 8

Yep

Answer 9

so thats it

Answer 10

@FutureMathProfessor

Answer 11

@whpalmer4

Answer 12

@SolomonZelman

Answer 13

You have points D(1,4) and F(7,1). You want to divide the line segment connecting them in a 2:1 ratio. If you have an \(a:b\) ratio, that means you go \(a\) part(s) out of every \(a+b\) parts. With a \(2:1\) ratio, there are \(3\) parts, and you'll go \(2\) out of every \(3\).

Because these are straight lines, with constant slope, dividing the line in a \(2:1\) ratio is exactly equivalent to dividing the change in \(x\) values in a \(2:1\) ratio, and dividing the change in \(y\) values in a \(2:1\) ratio.

Change in \(x\) values from \((1,4)\) to \((7,1)\) is \(7-1 = 6\). What is \(\frac{2}{3}*6\)? Add that to the starting \(x\) value of \(1\) to get your \(x\) value for T.

Change in \(y\) values from \((1,4)\) to \((7,1)\) is \(1-4 = -3\). What is \(\frac{2}{3}*(-3)\)? Add that to the starting \(y\) value of \(4\) to get your \(y\) value for T.

Answer 14

is that the whole answer

Answer 15

No, you have to do the work! I told you HOW to do the work. If you're only interested in having someone tell you the answer, stop tagging me.

Answer 16

i never said that

Answer 17

And I never said you did. However, if you had done as I requested, you should be able to judge for yourself if you were done with the problem. It is just as important to be able to read the problem statement and decide if you have answered it as it is to be able to do the calculations.