Answer:
Here we need to use:
[tex]\sqrt{x^2} = |x|[/tex]
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Then the distance between:
(-3, -5) and (9, -5) is just:
[tex]D = \sqrt{(-3 - 9)^2 - (-5 - (-5))^2} \\\\D = \sqrt{(-3 - 9)^2} = |-3 - 9|[/tex]
because both numbers inside the absolute value, we can rewrite it as:
|-3 - 9| = |-3| + |-9| = |-3| + |9| = 12
So, by finding the distance between (−3, −5) and (9, −5), we got the given expression, in this way we prove that the given expression represents the distance between these points.
