Find the distance from the point (-5.2,-3) to the (a) xy-plane (b) x z -plane (c) yz-plane (d) x

step 1 In this problem, we have to use our knowledge of three -dimensional space to find the distance f

Find the distance from the point (-5.2,-3) to the (a)...

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Key Concepts

Coordinate Systems

Coordinate systems provide a framework for representing points in space using numerical coordinates. In three?dimensional space, a common system is the Cartesian coordinate system, where points are identified by three numbers corresponding to the x, y, and z axes.

Coordinate Planes

Coordinate planes are flat surfaces defined by setting one of the three coordinate values to zero. For example, the xy-plane is defined by z = 0, the xz-plane by y = 0, and the yz-plane by x = 0. These planes serve as reference surfaces for measuring distances and positions in 3D space.

Distance from a Point to a Plane

The distance from a point to a coordinate plane that is defined by one coordinate being zero is simply the absolute value of the coordinate that is omitted in the plane’s equation. For instance, the distance to the xy-plane is the absolute value of the z-coordinate of the point.

Distance from a Point to a Line (Axis)

Calculating the distance from a point to a coordinate axis (which is a line) involves using the Euclidean distance formula in the plane perpendicular to that axis. For example, the distance from a point to the x-axis is found by taking the square root of the sum of the squares of the y and z coordinates.

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