Given the points P(-2, 5, 9) and Q(3, -2, 4)
Let the plane YZ-plane divide line segment PQ at point G(0, y, z) in the ratio m : n.
0
The coordinates of the point G which divides the line joining points A(x1, y1, z1) and B(x2, y2, z2) in the ratio m:n is given by
Here, we have m : n
x1 = -2 y1 = 5 z1 = 9
x2 = 3 y2 = -2 z2 = 4
By using the above formula, we get,
Now, this is the same point as G(0, y, z),
As the x-coordinate is zero,
[Cross Multiplying]
3m – 2n = 0 × (m + n)
3m – 2n = 0
3m = 2n
\(\frac{m}{n}=\frac{2}{3}\)
Therefore, the ratio in which the plane-YZ divides the line joining A & B is 2 : 3
