Question

In what ratio does XY- plane divide the line joining the points ( 2,4,2 ) and (2, 5,-4)​

Answer 1

Answer: 1 : 2

There are two points A(2,4,2) and B(2,5,-4) in a 3d space, We have to find the ratio in which the XY plane divides the line joining the two points (AB).

First of all, It is clear that the distance from the z-axis on XY plane will always be zero i.e., the point on the line at which the XY plane intersects is (x, y, 0)

Now, Using the section formula in 3d geometry we can find the ratio easily.

Let the ratio be k : 1, Now

For the z cordinate,

⇒ z = (kz₂ + z₁) / (k + 1)

Because, The z cordinate of the intersecting point is zero, Hence

⇒ 0 = { k(-4) + (2) } / (k + 1)

⇒ -4k + 2 = 0

⇒ 2 = 4k

⇒ k = 1 / 2

So, The ratio in which the XY plane divides the line is 1:2 .

Some Information:

• Distance formula in 3D

Let any two distinct points in a space be A and B, where A = (x₁, y₁, z₁) and B = (x₂, y₂, z₂) then the distance between the two points is given by:

⇒ √{ (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² }

Answer 2

Answer:

1:2

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