Question

For three points, X, Y and Z, to be collinear, which of these conditions should be true? Select all that apply.

• A.
  $XY+YZ=XZ$
• B.
  $XY+YZ>XZ$
• C.
  $XZ-YZ>XY$
• D.
  $XZ+YZ=XY$

Answer 1

Answer: (A), (D)

$XZ+YZ=XY$
The sum of any two of the distances is equal to the third distance, the points are said to be collinear.

We are given 3 points X, Y and Z.

The distances between the points are XY, YZ and XZ.

So, for points X, Y and Z to be collinear, we have,

$XY+YZ=XZOrYZ+XZ=XYOrXY+XZ=YZ\text{These can further be written as:}XZ-YZ=XYOrXY-XZ=YZOrYZ-XZ=XY$