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

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Explanation:

The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).

Answer 2

Here we need to use:

`√(x^2) = |x|`

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

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

Then the distance between:

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

`D = √((-3 - 9)^2 - (-5 - (-5))^2) \\\\D = √((-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.