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Lol i'm waiting for CPhill.. he'll know how to explain it down to me.

I didn't think of that approach...but.....we want to find the midpoint  of AB  and then find the midpoint of A  to this calculated midpoint

WTH??

i don't think so

If it is then I will explain how I got it.

I am not 100% sure if this answer is correct but is the answer \(\frac{7}{6}\)

Oh, ok, I get it! Thanks so much!

OK....we have

[  - 6  +  (15 - - 6)(2/3),  19  + (-5 - 19)(2/3)  ]

[ - 6  +  (21)(2/3), 19 + (-24)(2/3) ]

[ - 6  + 14,  19  -  16 ]

(8, 3)

@CPhill can we just find the midpoint and divide the answer by 4??

What we are looking for is the point that is   1 / (1 + 3)  = 1/4  the distance from A to B

This can be calculated as follows :

[ 5   +  (8 - 5)/4  ,  6  + (-2 - 6)/4  ]  =

[ 5  + 3/4 , 6 +  -8/4  ]

[ 5 + 3/4,  6  - 2 ]

( 23/4,  4 )

I wish I could help u guys but I forgot how to solve these type of questions cuz I used to solve them in grade 9 and 10

So the coordinates of A and B are basically finding the mid-point of RS and ST.

1^st  to find the mid-point u use the formula \((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

The mid-point of RS is,

\((\frac{0+2a}{2}, \frac{0+2b}{2})\) 

\((\frac{2a}{2}, \frac{2b}{2})\)

\((a,b)\)

\((a,b)\) are the coordinates of A.

Now the midpoint of ST is,

\((\frac{2a+2c}{2}, \frac{2b+2d}{2})\)

\((\frac{2(a+c)}{2}, \frac{2(b+d)}{2})\)

\(((a+c),(b+d))\)

\(((a+c)+(b+d))\) are the coordinates of ST.

I didn't quite understand what the slope part means

Yep, I did. Sorry: Given \(R(-6,19)\) and \(S(15,-5)\), what are the coordinates of the point on segment \(\overline{RS}\)  two-thirds of the distance from \(R\) to \(S\) ?

I judged it to be the "Best Answer".....because...it WAS  !!!!

Good job,  Rauhan.....!!!

y=−2/3x+5

A line perpendicular to this will have a negative reciprocal slope, i.e.,  3/2

So   we have

y  =  (3/2)(x  - 8)  +  1

y  =  (3/2)x  - 12  +  1

y  =  (3/2)x  - 11

It's easier to find 1/3 of the distance from R to S.....so we have

[ -6  +  (15 - - 6)/3   , 19  +  ( -5 - 19)/ 3  ]  =

[ -6  + 21/3,  19  +  -24/3 ]  =

[ -6   + 7,  19  - 8  ]  =

(1, 11)

Same answer as Melody's  ???

Did you leave something out, tertre ???

Finally, after a very long time, my answer was chosen as the best answer; worked so hard for this

Oh, I get it now! Thanks again, CPhill! 

Look  at the graph, here :

https://www.desmos.com/calculator/sdppfsq0xq

The three intersection points  occur at  (5,-2), (10, 0)  and (-2, 12)

And these form a triangle......

Let us  consider  the base to be the segment joining  (10,0)  and (-2,12)

And the length  of this base  =  sqrt [ (-2 -10)^2  + 12^2]  =   sqrt (288)  =  12sqrt(2)

And the altitude of this triangle can be drawn from (5, -2)  perpendicular to the line x + y  - 10 = 0

And this distance can be calculated as follows :

Altitude  =    abs   [  ax + by  -  10 ]  /  sqrt ( a^2  + b^2 ) 

Where (a, b)  = (1, 1)    and  (x, y)  = (5, -2)

So we have

Altitude  =  abs  [ 5  +  (-2)   -  10] / sqrt [  1^2 + 1^2 ]  =

abs  [ -7]  /  sqrt [ 2]   =      7 / sqrt (2)

So.....this area  =  (1/2)base * height  =

(1/2)(12*sqrt(2) ) *  7 / sqrt (2)   =   42 units^2

So the formula for finding the midpoint is 

\((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

Substituting the values gives

\((\frac{-1+3}{2}, \frac{9+8}{2})\)

\((1,\frac{17}{2})\)

\((1,8.5)\)

is the answer (1,11)? If so, it's wrong...

If pure water is added, the  %  of   sulphuric acid   =   0%

So....we have the following equation :

400(.20)  + 240(.43)  + 350(.66)  +  0x =   .10(400 + 240 + 350  + x)

80  +  103.2  + 231    =   .10x  +  .10( 400 + 240  +  350)

414.2      =  .10x   +  .10(990)

414.2  =  .10x  +  99           subtract  99 from both sides

315.2  =  .10x        divide both sides by .10

3152  =  x

So.....3152g  of pure water should be added

I understood that

Wolfram/Alpha claims that it can solve chemical equations. Try one of your equations and see if it gives you a meaningful answer. If it does, then I can give you the steps it uses to arrive at that answer. Good luck.

Divide the interval  S(15,-5)  R(-619)  in the ratio  2:1

\((\frac{1*15+2*-6}{3},\frac{1*-5+2*19}{3})\\ =(\frac{15-12}{3},\frac{-5+38}{3})\\ =(\frac{3}{3},\frac{33}{3})\\ =(1,11)\)