What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

The coordinates of the points A and B are not given. We'll assume: A(3,1) B(12,-5)

The coordinates of E are (6,-1)

Step-by-step explanation:

Partition of a Segment

The length of segment directed from A(xa,ya) to B(xb,yb) can be decomposed in its x,y coordinates:

If a point E is to be in the segment and partition it into a ratio 1:2, then

\displaystyle \frac{x_{AE}}{{x_{EB}}=\frac{y_{AE}}{{y_{EB}}=\frac{1}{2}

But

Then we set the equation:

Operating and rearranging

Solving

Similarily

The coordinates of E are (6,-1)

77

step-by-step explanation: