Question

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?

Answer 1

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

Answer:

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:

$x_{AB}=x_b-x_a$

$y_{AB}=y_b-y_a$

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

$x_{AE}=x_e-x_a$

$y_{AE}=y_e-y_a$

$x_{EB}=x_b-x_e$

$y_{EB}=y_b-y_e$

Then we set the equation:

$\frac{x_{AE}}{{x_{EB}}=\frac{1}{2}$

$2(x_e-x_a)=x_b-x_e$

Operating and rearranging

$3x_e=x_b+2x_a$

Solving

$\displaystyle x_e=\frac{x_b+2x_a}{3}=\frac{12+6}{3}$

$x_e=6$

Similarily

$\displaystyle y_e=\frac{y_b+2y_a}{3}=\frac{-5+2}{3}$

$y_e=-1$

The coordinates of E are (6,-1)

Answer 2

Answer:(-2,5)

Step-by-step explanation: took the test