Question

I am totally lost with this. can someone help ? & explain how to do it... :O

A point Q on a segment with endpoints A (2, -1) and C (4, 2) partitions the segment in a 3:1 ratio. Find Q

Answer 1

3:1 ratio means you divide the line between A and C into 4 equal parts, then start at point A and move 3 parts along it and put Q there.

Answer 2

in turns out to be relatively easy. you can do the "x" distance and the "y" distance separately.

first, find the distance from A to C in the x-direction. can you do that ?

Answer 3

ill try :) hold on

Answer 4

ok i used the distance formula \[d=\sqrt{(x2-x1)^2 + (y2-y1)^2}\] and i got sq root of 13 = 3.6

Answer 5

that is not the one your asking me for right ?

Answer 6

try this (hopefully it attached ok!)

Answer 7

using the distance formula is a hard way to do this.

just find the difference is the x values (as the first step) what do you get?

Answer 8

It didn't; there's a formula that goes with it that explains how to do all of these with no problems with the ratio. It's really easy!!

Answer 9

If \((x_1, y_1)\) and \((x_2, y_2)\) are the two points then,
the x-distance = \(x_2-x_1\)
the y-distance = \(y_2-y_1\)

Answer 10

x- distance is 2 and y-distance is 3 ?

Answer 11

correct.

Answer 12

yes. x distance is 2.
now divide that distance by 4 to get 2/ 4 = 1/ 2
move 3 "parts" or 3* 1/ 2 = 1 1 /2
add 1 1 /2 to the x value of point A
that gives you the X value of C

Answer 13

do the same for y

y distance is 3
divide by 4 to get 3 /4
move 3 of these, i.e. 3 * 3 /4 = 9/ 4
add 9/ 4 to the y value of A to get the y value of C

Answer 14

that gives you the x value of *Q*
that gives you the y value of *Q*

Answer 15

so i have to do this :
since the x-distance is 2 i divide it by 4
2 /4 = 0.5
3 x 0.5 = 1.5
& then im lost -.-

Answer 16

Add that 1.5 to the x-value of point A to get the x-value of point Q.

Answer 17

1.5 + 2 = 3.5 ?

Answer 18

Yes. Do the same for y.

Answer 19

so i have to do this :
since the x-distance is 2 i divide it by 4
2 /4 = 0.5
3 x 0.5 = 1.5
1.5 + 2= 3.5

y-distance is 3
3/4 =0.75
3 x 0.75=2.25
then 2.25 + 3 = 5.25 ?

Answer 20

y-distance is 3.
divide by 4
multiply by 3

Answer 21

3/4 = 0.75
3 x 0.75 = 2.25 ?

Answer 22

yes 2.25 + (-1) = 1.25

Answer 23

***then 2.25 + 3 = 5.25 ?***

where did you get the 3. You add the 2.25 to the y-value of point A

Answer 24

i got the 3 from the y- distance. 2.25 + (-1) = 1.25 oohhhh

Answer 25

just to make sure
2 /4 = 0.5
3 x 0.5 = 1.5
1.5 + 2= 3.5

y-distance is 3
3/4 =0.75
3 x 0.75=2.25
then 2.25 + (-1) = 1.25 ?

Answer 26

Correct. The coordinates of Q are: (3.5, 1.25)
or
(7/2, 5/4)

Answer 27

Cool! Thanks for helping ! & explaining ^.^
i understood everything

Answer 28

You are welcome.