Question

​On the directed line segment from R to S on the coordinate plane ​above, what are the coordinates of the point that partitions the ​segment in the ratio 2 to 3?
The coordinates for R is (-6,4) and S is (8,-4)

Answer 1

Answer:

$\left(\displaystyle -\frac{2}{5},\frac{4}{5}\right)$

Step-by-step explanation:

Proportions

The coordinates of the point R are (-6,4) and the coordinates of the point S are (8,-4). We must find the coordinates of a point P(x,y) such that the ratio of segment RP to segment PS is 2/3. Let's find the coordinates separately. In the x-axis:

$\displaystyle \frac{-6-x}{x-8}=\frac{2}{3}$

Operating and rearranging

$-18-3x=2x-16$

Solving

$\displaystyle x=-\frac{2}{5}$

Now for the y-axis

$\displaystyle \frac{4-y}{y+4}=\frac{2}{3}$

Operating and rearranging

12-3y=2y+8

Solving

$\displaystyle y=\frac{4}{5}$

Thus, the point that partitions the segment in the ratio 2 to 3 is

$\left(\displaystyle -\frac{2}{5},\frac{4}{5}\right)$