Question

Which pair of points forms a vertical line segment that is 4 units long?

Answer 1

In a Cartesian coordinate system, a vertical line segment always is parallel to the y-axis, so we have this coordinate system in the figure below. We need to find a pair of points that is 4 units long.

So, this pair of points are in the general forms as follow:

$P_{1}( x_{1}, y_{1})$
$P_{2}( x_{2}, y_{2})$

Given that the straight line is vertical, then:

$x_{1}=x_{2}$
 
Then the point 2 is modified as:

$P_{2}( x_{1}, y_{2})$

We need to find a point which is 4 units long, so:

$d = y_{2} - y_{1} = 4$
∴ $y_{2} = 4+ y_{1}$

So, we can find infinite points given a value of $y_{1}$, therefore if:

$y_{1} = 2$ then:

∴ $y_{2} = 6$

Thus, if $x_{1} = 1$ then a pair of points are:

$P_{1}(1,2)$
$P_{2}(1,6)$