Answer:
[tex](a)\ (0, -2)\ and\ (0, 9)[/tex]
They lie on the same horizontal line
Distance = 11 units
[tex](b)\ (11, 4)\ and\ (2, 11)[/tex]
They do not lie on the same vertical or horizontal line
Step-by-step explanation:
Given
[tex](a)\ (0, -2)\ and\ (0, 9)[/tex]
[tex](b)\ (11, 4)\ and\ (2, 11)[/tex]
Required
Determine if the points lie on the same vertical or horizontal line
A point is represented as: [tex](x,y)\\[/tex]
Using the above illustration, we have:
[tex](a)\ (0, -2)\ and\ (0, 9)[/tex]
The above have the same x values (0), hence they lie on the same horizontal line.
The distance between them is:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]d = \sqrt{(0-0)^2 + (-2 - 9)^2}[/tex]
[tex]d = \sqrt{0^2 + (-11)^2}[/tex]
[tex]d = \sqrt{0 + 121}[/tex]
[tex]d = \sqrt{121}[/tex]
[tex]d = 11[/tex]
The distance between them is 11 units
[tex](b)\ (11, 4)\ and\ (2, 11)[/tex]
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
