What is the vertical distance of $(-6,-4)$ from $0$?

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megumina41 megumina41

05-11-2026
Mathematics

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What is the vertical distance of $(-6,-4)$ from $0$?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T14:13:56-05:00

Identify the y-coordinates of the point $(-6, -4)$ and the origin $(0, 0)$, which are $-4$ and $0$, respectively.
Apply the vertical distance formula, which is the absolute difference between the two y-coordinates: $|y_1 - y_2|$.
Compute the result: $|-4 - 0| = |-4| = 4$.
Final answer: $\boxed{4}$ units.

Explanation

Define the vertical distance formula.

To find the vertical distance between the point $P = (-6, -4)$ and the origin $O = (0, 0)$, we need to look at the vertical components of their positions, which are represented by their y-coordinates. The y-coordinate of the point $P$ is $-4$, and the y-coordinate of the origin $O$ is $0$. The vertical distance is defined as the absolute difference between these two y-values.

Calculate the vertical distance.

The vertical distance $d_v$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
\[d_v = |y_1 - y_2|\]
Substituting the y-coordinates of our points, where $y_1 = -4$ and $y_2 = 0$, we get:
\[d_v = |-4 - 0|\]
\[d_v = |-4|\]
Since the absolute value of $-4$ is $4$, the vertical distance is $4$ units.

Examples

If a submarine is at a depth of 400 meters below sea level, its position could be represented as $(x, -400)$ relative to a reference point on the surface at $(0, 0)$. The vertical distance from the surface is the absolute value of the depth, calculated as $|-400 - 0| = 400$ meters. This shows how coordinate geometry helps in calculating physical distances in vertical space.