What is the fraction you used? Given the points A(3, 4) and B (6, 10), find the pordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.

Question

asked Aug 23, 2023 119k views

1 Answer

Nietzsche · Answer 1 · 2023-08-29T21:45:50+0000

Given the points A(3, 4) and B (6, 10), find the pordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.

we have that

AP/AB=2/(2+1)

AP/AB=2/3

step 1

Find the distance AB in the x-coordinate (ABx)

ABx=6-3=3 units -----> subtract the x-coordinates

we have that

AP/AB=2/3

so

APx/ABx=2/3

APx is the distance AP in the x-coordinate

substitute the given value in the expression above

APx/3=2/3

APx=2 units

Find the x coordinate of point P

Px=AX+APx

Px=3+2=5

step 2

Find the distance AB in the y-coordinate (ABy)

ABy=10-4=6 units (subtract the y-coordinates)

we have that

AP/AB=2/3

so

APy/ABy=2/3

substitute the given value

APy/6=2/3

APy=4 units

Find the y-coordinate of point P

Py=Ay+APy

Py=4+4=8

therefore