Find the coordinates of point q that lies along the directed line segment from r(-2, 4) to s(18, -6) and partitions the segment in the ratio of 3: 7.

Find the distance between them
distance between (x1,y1) and (x2,y2) is


so distance between (-2,4) and (18,-6) is





D=10√5

so in ratio 3:7
3+7=10
3/10 of 10√5 is 3√5

I'm thinkin you want R then Q then S such that RQ:QS=3:7
so
distance from R to Q is 3√5
Q is (x,y)
R is (-2,4)
D=3√5



square both sides



now, ithas to be on the line that R and S are on
do some simple math
slope is rise/run=-10/20=-1/2
y=-1/2x+b
4=-1/2(-2)+b
4=1+b
3=b
y=-1/2x+b

sub that for y in our other equation ()


I'm too lazy to show you expanstion and whatnot so I'll give you the solution
we get (after some manipulation)
0=x²+4x-32
what  2numbers multiply to get -32 and add to get 4?
-4 and 8
0=(x-4)(x+8)
set to zero

0=x-4
4=x

0=x+8
-8=x
but wait, -8 is not between -2 and 18 so it can't be

so x=4

remember, y=-1/2x+3
sub that to get y=-1/2(4)+3=-2+3=1

the point is (4,1)
apologies for mishap