Question

What are the coordinates of the point on the directed line segment from (-1,1) to (8, 10) that partitions the segment into a ratio of 2 to 1?

Answer 1

Point 1 = (x1,y1)= (-1,1)

Point 2 = (x2,y2)= (8,10)

xp,yp= ? (coordinates of the point)

a:b= 2:1

xp= x1+ a/a+b (x2-x1)

xp= -1+ 2/2+1 (8-(-1))

xp= -1+2/3 (8+1)

xp= -1+2/3(9)

xp= -1+ 6

xp= 5

yp= y1 + a/ a +b (y2-y1)

yp= 1 +2/3 (10-1)

yp =1+2/3 (9)

yp=1+6

yp=7

xp,yp = (5,7)