Question

Determine whether each given pair of endpoints lies on the same horizontal or vertical line.
If so, find the length of the line segment that joins the pair of points.
If not, explain how you know the points are not on the same horizontal or vertical line.
(3,-8) and (3,-1)

Answer 1

Given:

The pair of end points: (3,-8) and (3,-1).

To find:

Whether the given pair of endpoints lies on the same horizontal or vertical line.

Solution:

If the x-coordinates of pair of endpoints are same, then the pair of endpoints lies on the same vertical.

If the y-coordinates of pair of endpoints are same, then the pair of endpoints lies on the same horizontal.

The given endpoints are (3,-8) and (3,-1).

From the given endpoints, it is clear that the x-coordinates of the endpoints are same. So, the given endpoints lies on the same vertical line.

The length of the line segment that joins the pair of points is

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$D=\sqrt{(3-3)^2+(-1-(-8))^2}$

$D=\sqrt{(0)^2+(-1+8)^2}$

$D=\sqrt{(7)^2}$

$D=7$

Therefore, the given endpoints lies on the same vertical line and the length of the line segment is 7 units.