In what ratio is the line segment joining the points (−1,−1,−4) and (0,2,−5) is divided by the XY plane ?Also, find the co-ordinates of the point of division.
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Solution
Let the line segment formed by joining the points (−1,−1,−4) and (0,2,−5) is divided by the XY plane in the ratio k:1 at the point P, then the co-ordinates of P are
(−1k+1,2k−1k+1,−5k−4k+1)
But P lies in the XY plane,
∴z−co-ordinate is zero
⇒−5k−4k+1=0
⇒−5k−4=0
⇒5k=−4
⇒k=−45
Hence,XY plane divides the line segment AB in the ratio −45:1
i.e.,4:5 externally and the coordinates of the point of division are