Question

If x coordinate of a point on the line joining points (2, 2, 1) and (5, 1, -2) is 4, then its z co-ordinate will be ______

Options

• 1

• -1

• 2

• -2

Answer 1

If x coordinate of a point on the line joining points (2, 2, 1) and (5, 1, -2) is 4, then its z co-ordinate will be -1.

Explanation:

The equation of the line joining the points (2, 2, 1) and (5, 1, -2) is 

`(x - 2)/(5 - 2) = (y - 2)/(1 - 2) = (z - 1)/(-2 - 1)`

⇒ `(x - 2)/3 = (y - 2)/(-1) = (z - 1)/(-3)` ..............(i)

Since, x co-ordinate is 4

∴ It satisfies (i)

∴ `(4 - 2)/3 = (y - 2)/(-1) = (z - 1)/(-3)`

∴ `(z - 1)/(-3) = 2/3`

∴ 3z - 3 = -6

∴ z = -1