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

Complete question:

What are the $x-$ and $y-$ coordinates of point $E$, which partitions the directed line segment from $A\:(- 4,\:9)$ to $B\:(2,\:- 3)$ into a ratio of $1 : 2$.

Formula:

Let $R$ be the point that divides the line segment joining the points $A\:(x_{1},\:y_{1})$ and $B\:(x_{2},\:y_{2})$ into the ratio $l:m$ internally. Then the coordinates of

$\quad\quad \big(\frac{lx_{2}+mx_{1}}{l+m},\:\frac{ly_{2}+my_{1}}{l+m}\big)$

Solution:

The given points are $A\:(- 4,\:9)$ and $B\:(2,\:- 3)$.

Let $E$ be the point that divides the line segment $AB$ in the ratio $1 : 2$ internally.

Then the coordinates of $E$ be

$\quad\big(\frac{1(2)+2(-4)}{1+2},\:\frac{1(-3)+2(9)}{1+2}\big)$

$\to \big(\frac{2-8}{3},\:\frac{-3+18}{3}\big)$

$\to \big(\frac{-6}{3},\:\frac{15}{3}\big)$

$\to (-2,\:5)$

Answer: Therefore $(- 2,\:5)$ are the coordinates of the point $E$ that divides the line segment joining the points $A\:(- 4,\:9)$ and $B\:(2,\:- 3)$.

Option (C) is correct.

Read more on Brainly.in

Find the co-ordinates of a point which divides the line joining the points $(-3,\:9)$ and $(1,\:-3)$ internally in the ratio $2:3$.

https://brainly.in/question/16832096