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

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((mc+na)/(m+n),(md+nb)/(m+n)\right).`

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

`\left((5*(-15)+2*(-8))/(5+2),(5*(-13)+2*8)/(5+2)\right)\\\\\\=\left((-75-16)/(7),(-65+16)/(7)\right)\\\\\\=\left((-91)/(7),(-49)/(7)\right)\\\\=(-13,-7).`

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