Question

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Derive the coordinates of point R (x,y,z) dividing the line joining the points P(x1,y1,z1) and Q(x2,y1,z2) internally in the ratio m:n

Answer 1

Answer:Find coordinates of point which divides line segment joining points (1, –2, 3) and (3, 4, –5) in the ratio 2 : 3 internally, and externally.

Solution: Here m=2 & n=3. Coordinates of Point P when it divided m:n internally is

Px = (mx2 + nx1) / (m+n) = (2* 3 + 3 * 1)/(2+3) = 9/5

Py = (my2 + ny1) / (m+n) =(2* 4 + 3 * (-2))/(2+3) = 2/5

Pz = (mz2 + nz1) / (m+n) = (2* (-5) + 3 * 3)/(2+3) = -1/5

There coordinates of P are (9/5 , 2/5, -1/5)

Similarly in case the line is divided externally in ration m:n, then coordinates of Point P are

Px = (mx2 - nx1) / (m-n) = (2* 3 - 3 * 1)/(2-3) = -3

Py = (my2 - ny1) / (m-n) =(2* 4 - 3 * (-2))/(2-3) = -14

Pz = (mz2 - nz1) / (m-n) = (2* (-5) - 3 * 3)/(2-3) = 19

There coordinates of P are (-3,-14, 19)

Step-by-step explanation: