Answer:
Distance = 4
Step-by-step explanation:
Given the linear equation of line ℓ, y = 5 which is a horizontal line in which its slope, m = 0 (zero slope), and each of the x-coordinates along the line have the same y-coordinate of y = 5.
In order to determine the distance of the horizontal line from the given point Q, (0, 1), use the following distance formula:
[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]
Choose any x-coordinate to pair with the y-coordinate, y = 5. Let's use the y-intercept, (0, 5).
Let (x₁, y₁) = (0, 1)
(x₂, y₂) = (0, 5)
Substitute these values into the distance formula:
[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}[/tex]
[tex]d = \sqrt{(0 - 0)^{2} + (5 - 1)^{2}}[/tex]
[tex]d = \sqrt{(4)^{2}}[/tex]
[tex]d = \sqrt{16}[/tex]
d = 4
Therefore, the distance of line ℓ from point Q is 4.
