# Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

Let the line segment formed by joining the points P (-2, 4, 7) and Q (3, -5, 8) be PQ.

We know that any point on the YZ-plane is of the form (0, y, z).

Now, let R (0, y, z) divides the line segment PQ in the ratio k : 1.

Then,

Comparing this information with the details given in the question, we have

x1 = -2, y1 = 4, z1 = 7; x2 = 3, y2 = -5, z2 = 8 and m = k, n = 1

By section formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x1, y1, z1) and Q (x2, y2, z2) internally in the ratio m : n is given by:

So, we have

3k 2 = 0 3k = 2

Hence, the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8) is 2 :3.

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