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)

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:

Operating and rearranging

Solving

Now for the y-axis

Operating and rearranging

12-3y=2y+8

Solving

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

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.