Question

Explain why |−3| + |9| represents the distance between the points (−3Explain why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5)., −5) and (9, −5).

Answer 1

Answer:

Here we need to use:

$\sqrt{x^2} = |x|$

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

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

Then the distance between:

(-3, -5) and (9, -5) is just:

$D = \sqrt{(-3 - 9)^2 - (-5 - (-5))^2} \\\\D = \sqrt{(-3 - 9)^2} = |-3 - 9|$

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.