Question

Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2.

Answer 1

Answer:

X = [-8, 8] + 5/7·([-15, -13] - [-8, 8]) = [-13, -7]

Answer 2

Answer:  The required co-ordinates of the point X are (-13, -7).

Step-by-step explanation:  We are given the co-ordinates of the point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2.

We know that

the co-ordinates of a point that divides a line segment with end points (a, b) and (c, d) in the ratio m : n is given by

$\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).$

Therefore, the co-ordinates of the point X are given by

$\left(\dfrac{5\times(-15)+2\times(-8)}{5+2},\dfrac{5\times(-13)+2\times8}{5+2}\right)\\\\\\=\left(\dfrac{-75-16}{7},\dfrac{-65+16}{7}\right)\\\\\\=\left(\dfrac{-91}{7},\dfrac{-49}{7}\right)\\\\=(-13,-7).$

Thus, the required co-ordinates of the point X are (-13, -7).