Question

what are the ex and Y coordinates of point E, which partition the directed line segment from A to B into a ratio of 1:2?

Answer 1

Explanation:

The formula for this is the one we use when we are given the ratio the directed line segment is separated into as opposed to the point being, say, one-third of the way from one point to another. The 2 equations we use to find the x and y coordinates of this separating point are:

`x=(bx_1+ax_2)/(a+b)` and
`y=(by_1+ay_2)/(a+b)` where x1, x2, y1, y2 come from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in for x first:

`x=(2(2)+1(-4))/(1+2)=(4-4)/(3)=0` and then y:

`y=(2(-3)+1(9))/(1+2)=(-6+9)/(3)=(3)/(3)=1`

The coordinates of point E, then, are (0, 1).

Answer 2

(-1,3)

Explanation:

Mathematically, what we have to do here is to get the coordinates of the midpoint of the line AB

we have this as;

(x,y) = (x1 + y1)/2, (y1 + y2)/2

(x,y) = (-4+2)/2, (9-3)/2 = (-1, 3)