Find the distance from the point to
a. the originb. the z-axis.
I’d be very glad if you could help me
The points are 3,5,2
the distance to (0,0,0) is √(3^2+5^2+2^2)
For the distance to the z-axis, consider the point as lying in a plane perpendicular to the z-axis, at z=2.
The distance to (0,0,2) is √(3^2+5^2)
Of course! I'll be glad to help you find the distance from a given point to the origin and the z-axis.
To find the distance from the point (x, y, z) to the origin, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula in three-dimensional space is:
Distance = √((x - x₀)² + (y - y₀)² + (z - z₀)²),
where (x, y, z) represents the coordinates of the given point, and (x₀, y₀, z₀) represents the coordinates of the origin (0, 0, 0).
For example, let's say we have a point P(2, 3, 4). The coordinates of the origin are (0, 0, 0). By substituting these values into the distance formula, we get:
Distance = √((2 - 0)² + (3 - 0)² + (4 - 0)²)
= √(2² + 3² + 4²)
= √(4 + 9 + 16)
= √29.
Therefore, the distance from point P(2, 3, 4) to the origin is √29.
Now, to find the distance from a point to the z-axis, which is a vertical line passing through the origin, you need to consider only the x and y coordinates of the given point. So, the formula becomes:
Distance to z-axis = √((x - x₀)² + (y - y₀)²).
Using the same example, let's find the distance from point P(2, 3, 4) to the z-axis. Since the z-axis lies on x = 0 and y = 0, we have:
Distance to z-axis = √((2 - 0)² + (3 - 0)²)
= √(2² + 3²)
= √(4 + 9)
= √13.
Therefore, the distance from point P(2, 3, 4) to the z-axis is √13.
Remember to substitute the coordinates of the given point and the reference point (origin or z-axis) into the respective formulas to find the distances.