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)`