Question

Determine whether each given pair of end points 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.

Answer 1

`(a)\ (0, -2)\ and\ (0, 9)`

They lie on the same horizontal line

Distance = 11 units

`(b)\ (11, 4)\ and\ (2, 11)`

They do not lie on the same vertical or horizontal line

Explanation:

Given

`(a)\ (0, -2)\ and\ (0, 9)`

`(b)\ (11, 4)\ and\ (2, 11)`

Required

Determine if the points lie on the same vertical or horizontal line

A point is represented as:
`(x,y)\\`

• For a pair to lie on the same horizontal line, then they must have the same x values i.e.
  `(x,y_1)\ and\ (x,y_2)`

• For a pair to lie on the same vertical line, then they must have the same x values i.e.
  `(x_1,y)\ and\ (x_2,y)`

Using the above illustration, we have:

`(a)\ (0, -2)\ and\ (0, 9)`

The above have the same x values (0), hence they lie on the same horizontal line.

The distance between them is:

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)`

`d = √((0-0)^2 + (-2 - 9)^2)`

`d = √(0^2 + (-11)^2)`

`d = √(0 + 121)`

`d = √(121)`

`d = 11`

The distance between them is 11 units

`(b)\ (11, 4)\ and\ (2, 11)`

The above pair do not have the same x value and they do not have the same y value.

Hence, they do not lie on the same vertical or horizontal line