What's the coplanar point of w x y and z?
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To find the coplanar point of points w, x, y, and z, we need to determine if these points lie on the same plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions. If four points are coplanar, it means that they lie in the same plane.
To determine if four points are coplanar, we can use the concept of collinearity. Four points are coplanar if and only if they are all on the same line or lie on parallel lines. If any three of the points are collinear, then the fourth point will also be coplanar with them.
Here's how you can check if points w, x, y, and z are coplanar:
1. Take any three points, such as w, x, and y.
2. Determine if these three points are collinear. To do this, you can calculate the slopes between each pair of points.
- Calculate the slope between w and x: m₁ = (y₂ - y₁) / (x₂ - x₁)
- Calculate the slope between w and y: m₂ = (y₃ - y₁) / (x₃ - x₁)
- Calculate the slope between x and y: m₃ = (y₃ - y₂) / (x₃ - x₂)
If the slopes are equal (i.e., m₁ = m₂ = m₃), then points w, x, and y are collinear.
3. If points w, x, and y are collinear, we can check if point z lies on the same line by calculating the slope between z and any two of the other points and comparing them.
- Calculate the slope between z and w: m₄ = (y₂ - y₄) / (x₂ - x₄)
- Calculate the slope between z and x: m₅ = (y₃ - y₄) / (x₃ - x₄)
- Calculate the slope between z and y: m₆ = (y₃ - y₅) / (x₃ - x₅)
If any of the slopes m₄, m₅, or m₆ is equal to m₁ (the slope between w and x), then points w, x, y, and z are coplanar. Otherwise, they are not coplanar.
Note: Ensure that the coordinates of points w, x, y, and z are given accurately for the calculations.