What are the coordinates of point P on the directed line segment from R to Q such that P is 5/6 the length of the line segment from R to Q? Round to the nearest tenth, if necessary.

Step-by-step explanation: We are to find the coordinates of point P on the directed line segment from R to Q such that P is 5/6 the length of the line segment from R to Q.

We are to find the co-ordinates of point 'P'.

The ratio in which the point 'P' dives the line segment RQ will be

[tex]m:n=5:1.[/tex]

The co-ordinates of the end-points of line segment RQ are

R(4, -1) and Q(-5, 3).

If a point 'H' divides a line segment with end points (p, q) and (s, t) in the ratio m : n, then the co-ordinates of the point 'H' are

[tex]H=\left(\dfrac{ms+np}{m+n},\dfrac{mt+nq}{m+n}\right).[/tex]

Therefore, the co-ordinates of point 'P' are

[tex]\left(\dfrac{5\times (-5)+1\times 4}{5+1},\dfrac{5\times 3+1\times (-1)}{5+1}\right)\\\\\\=\left(\dfrac{-25+4}{6},\dfrac{15-1}{6}\right)\\\\\\=\left(\dfrac{-21}{6},\dfrac{14}{6}\right)\\\\\\=(-3.5,2.3).[/tex]

Thus, the required co-ordinates of the point 'P' are (-3.5, 2.3).

joaobezerra joaobezerra · Answer 2 · 2021-10-15T16:57:57+02:00

The coordinates of P are: [tex]P\left(\frac{5}{3},-\frac{1}{3}\right)[/tex].

Initially, we consider the coordinates of P as P(x,y).
The other points are: Q(-5,3) and R(4,-1).
Point P is 5/6 of the length of line segment of R to Q, thus:

[tex]P - Q = \frac{5}{6}(R - Q)[/tex]

This is used to find both the x-coordinate and the y-coordinate of P, replacing the x and y-coordinates of Q and R.

Find x:

[tex]P - Q = \frac{5}{6}(R - Q)[/tex]

[tex]x - (-5) = \frac{5}{6}(4 - (-4))[/tex]

[tex]x + 5 = \frac{40}{6}[/tex]

[tex]x = \frac{40}{6} - \frac{30}{6}[/tex]

[tex]x = \frac{10}{6}[/tex]

[tex]x = \frac{5}{3}[/tex]

Find y:

[tex]P - Q = \frac{5}{6}(R - Q)[/tex]

[tex]y - 3 = \frac{5}{6}(-1 - 3)[/tex]

[tex]y - 3 = -\frac{20}{6}[/tex]

[tex]y = -\frac{20}{6} + \frac{18}{6}[/tex]

[tex]y = -\frac{2}{6}[/tex]

[tex]y = -\frac{1}{3}[/tex]

The coordinates of P are: [tex]P\left(\frac{5}{3},-\frac{1}{3}\right)[/tex].

A similar problem is given at https://brainly.com/question/4854238