Question

Calculate the distance of a point with Cartesian coordinates (-4.51 m, -1.74 m) to the origin (0, 0) in units of meters.

Answer 1

The distance of the point with Cartesian coordinates (-4.51 m, -1.74 m) to the origin (0, 0) is approximately 4.76 meters.

Step-by-step explanation:

In order to find the distance between the point (-4.51 m, -1.74 m) and the origin (0, 0), we can use the distance formula from Euclidean geometry. The distance (d) between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

`\[ d = √((x₂ - x₁)² + (y₂ - y₁)²) \]`

In this case, the coordinates of the point (-4.51 m, -1.74 m) can be denoted as (x₁, y₁) and the coordinates of the origin (0, 0) as (x₂, y₂). Plugging in the values:

`\[ d = √((0 - (-4.51))² + (0 - (-1.74))²) \]`

`\[ d = √((-4.51)² + (-1.74)²) \]`

`\[ d = √(20.3401 + 3.0276) \]`

`\[ d = √(23.3677) \]`

`\[ d ≈ 4.76 \, \text{m} \]`

Therefore, the distance is approximately 4.76 meters. This result is obtained by applying the Pythagorean theorem to the differences in the x and y coordinates of the two points, resulting in the length of the hypotenuse, which represents the distance between the point and the origin in a Cartesian coordinate system.