PLZ HELP ASAP DIVIDE LINE SEGMENTS LAST ONE

AB/AC=2:7→AB/AC=2/7→AB=(2/7)AC
Taking:
Initial point: A=(0,-8)=(xi,yi)→xi=0, yi=-8
Point P=B=(2,-4)=(x,y)→x=2, y=-4
Final point: C=(xf, yf)=?

The proportion r=AB/BC
AB=(2/7)AC
BC=AC-AB=AC-(2/7)AC=(1-2/7)AC={[7(1)-2]/7}AC=[(7-2)/7]AC→
BC=(5/7)AC

r=AB/BC=[(2/7)AC] / [(5/7)AC]=(2/7)/(5/7)=(2/7)*(7/5)=(2*7)/(7*5)→
r=2/5=0.4

x=(xi+r*xf)/(1+r)
x=2, xi=0, r=0.4, xf=?
2=(0+0.4*xf)/(1+0.4)
2=0.4*xf/1.4
1.4*2=1.4*0.4*xf/1.4
2.8=0.4*xf
2.8/0.4=0.4*xf/0.4
7=xf
xf=7

y=(yi+r*yf)/(1+r)
y=-4, yi=-8, r=0.4, yf=?
-4=(-8+0.4*yf)/(1+0.4)
-4=(-8+0.4*yf)/1.4
1.4*(-4)=1.4*(-8+0.4*yf)/1.4
-5.6=-8+0.4*yf
-5.6+8=-8+0.4*yf+8
2.4=0.4*yf
2.4/0.4=0.4*yf/0.4
6=yf
yf=6

Point final C=(xf, yf)→C=(7,6)

Answer: C=(7,6)