The cartesian coordinates of a point in the xy plane are x = −8.09 m, y = −4.3 m. Find the distance r from the point to the origin. Answer in units of m.
To find the distance from a point to the origin, you can use the distance formula in a two-dimensional plane. The distance formula is given by:
r = √((x - x₀)² + (y - y₀)²)
where (x₀, y₀) represents the coordinates of the origin, and (x, y) represents the coordinates of the point.
In this case, the coordinates of the origin are (0, 0), and the coordinates of the point are (x = -8.09 m, y = -4.3 m). Plugging these values into the distance formula, we get:
r = √((-8.09 - 0)² + (-4.3 - 0)²)
Simplifying:
r = √((-8.09)² + (-4.3)²)
r = √(65.4881 + 18.49)
r = √(83.9781)
r ≈ 9.17 m
Therefore, the distance from the point (-8.09 m, -4.3 m) to the origin is approximately 9.17 meters.
To find the distance, r, from the point to the origin, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the x and y coordinates of the point as the two sides of a right triangle, with the origin as the right angle. So, we can use the formula:
r^2 = x^2 + y^2
Given that x = -8.09 m and y = -4.3 m, we can substitute these values into the formula:
r^2 = (-8.09 m)^2 + (-4.3 m)^2
Simplifying the equation:
r^2 = 65.7281 m^2 + 18.49 m^2
r^2 = 84.2181 m^2
Take the square root of both sides to solve for r:
r = sqrt(84.2181 m^2)
r ≈ 9.1734 m
Therefore, the distance, r, from the point to the origin is approximately 9.1734 meters.