Explain why the set of points (x, y, z) equidistant from (5, 9, 0) and (-5, 7, 4) is a plane. Select the correct explana

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Explain Why The Set Of Points X Y Z Equidistant From 5 9 0 And 5 7 4 Is A Plane Select The Correct Explana 1 (299.15 KiB) Viewed 36 times

Explain why the set of points (x, y, z) equidistant from (5, 9, 0) and (-5, 7, 4) is a plane. Select the correct explanation. Because in three dimensions, each point on a plane is equidistant from a given point, so that if the distances from both points are equal, the plane is equidistant from both points. Because in two dimensions, the set of points located at a distance r from the two points is a line, and considering all possible values of r produces a plane. O Because in two dimensions, the set of points equidistant from two points is a plane. Because in two dimensions, the set of points equidistant from two points is a line, and the result of rotating it through the third dimension with respect to the segment between the points is a plane. Find the equation of this plane. Hint: This can be done in two ways. The first one is to use the distance formula to equate the distances between (x, y, z) and the given points, simplifying the result to obtain the equation of the plane. The second one is to find a point on the plane and a vector normal to the plane and use the answer to find the equation of the plane. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation: Question Source: Sullivan 2e Calculus Publisher: W.H. Freeman