Question

Point C is located at (1, 2) and point D is located at (−4, −2). Find the x value for the point that is 1 over 4 the distance from point C to point D.

−0.25
3.25
−3.75
1.25

Answer 1

so where do you think the point "x" is at there?

or where would more or less would be in that graph

Answer 2

here? idk >.<

Answer 3

@jdoe0001

Answer 4

hmmm well... close
is 1/4 FROM C to D

so

so notice the picture
"x" is located from C to D 1/4 of the way
that means that CX is 1/4 and XD is 3/4

so XD is 3 times bigger than CX

or we can say that XD is at a 3:1 ratio to CX

or the other way around, that CX is at 1:3 ratio to XD

right?

Answer 5

right

Answer 6

so... let us use the ratio for those two sides
a ratio of 1:3 from CX to XD
thus gimme one sec

Answer 7

\(\bf \textit{internal division of a line segment}
\\ \quad \\

C(1,2)\qquad D(-4,-2)\qquad
ratio1=1\qquad ratio2=3\qquad 1:3\\ \quad \\ \quad \\

\cfrac{C\cancel{ X }}{\cancel{ X }D}=\cfrac{1}{3}\implies
3\cdot C=1\cdot D\quad \implies
3(1,2)=1(-4,-2)
\\ \quad \\

{\color{brown}{ X=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}\\ \quad \\

\qquad thus\qquad \\ \quad \\

X=\left(\cfrac{(3\cdot 1)+(1\cdot -4)}{1+3}\quad ,\quad \cfrac{(3\cdot 2)+(1\cdot -2)}{1+3}\right)\)

Answer 8

\[\frac{ 7 }{ 4 } , \frac{ 8 }{ 4 }\] ?

Answer 9

it comes out to that?

Answer 10

well.. check your sum again

Answer 11

1 * -4 = -4
1 * -2 = -2

Answer 12

oh instead of 7 it would be -1

Answer 13

and instead of 8 it would be 4

Answer 14

@jdoe0001

Answer 15

well... yes.... the first coordinate is off as well though

recheck them both, see what you get

Answer 16

i still got -1/4 , 4/4

Answer 17

well... that's different than what you posted earlier though

but that's correct, -1/4 and 4/4 or -1/4 and 1 :)

Answer 18

so how do i get one of the answer choices?

Answer 19

@jdoe0001

Answer 20

is it D?

Answer 21

@bibby

Answer 22

HI there, you still need help here?

Answer 23

yes

Answer 24

he never finished explaining

Answer 25

Start from the beginning or continue where you left off with the other helper?

Answer 26

all ik is that he made me solve this equation and i got -1/4 , 4/4

Answer 27

I didn't look back but was it this formula:

Answer 28

Ah wait I see what you did.

Answer 29

So yes, you basically have this already done. Your coordinates are (-1/4,1) and th x coordinate is what you need for this question. -1/4 is the same as -0.25. Therefore it is A.

Answer 30

omg thank you so much!!!!!

Answer 31

No need to thank me, you did all of the work! xD