Question

What are the coordinates of point P on a directed line segment from R to Q such that P is 5/6 the length of the line segment.

Answer 1

Answer:

$P = [-3/5,2.33]$

Step-by-step explanation:

Given

See attachment for line segment RQ

$P = \frac{5}{6}$ of RQ

Required

The coordinates of P

Using line segment ratio formula, we have:

$P = [\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n}]$

If P is at:

$P = \frac{5}{6}$

Then:

$m : n = \frac{5}{6} : 1 -\frac{5}{6}$

Solve

$m : n = \frac{5}{6} : \frac{6-5}{6}$

$m : n = \frac{5}{6} : \frac{1}{6}$

Multiply by 6

$m : n = \frac{5}{6} *6: \frac{1}{6} * 6$

$m : n = 5 : 1$

By comparison

$m=5\ \& n = 1$

From the attached line segment

$R(x_1,y_1) = (4,-1)$

$Q(x_2,y_2) = (-5,3)$

So, we have:

$P = [\frac{5*-5 + 1*4}{5+1},\frac{5*3 + 1*-1}{5+1}]$

$P = [\frac{-25 + 4}{6},\frac{15 -1}{6}]$

$P = [\frac{-21}{6},\frac{14}{6}]$

$P = [-3/5,2.33]$