Question

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.

Answer 1

All late but the answer is (-3.5, 2.3) :)

Answer 2

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

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

$m:n=5:1.$

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

$H=\left(\dfrac{ms+np}{m+n},\dfrac{mt+nq}{m+n}\right).$

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

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

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