identify the distance between the points (2,4,12) and (7,4,0), and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary. PLEASE HELP ASAP
Answers
Answer:
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The distance between the given points is 13 units and the coordinates of the midpoint of the segment is (4.5, 4, 6)
What is 3-dimensional geometry?3D geometry refers to the mathematics of shapes in three-dimensional space and consists of 3 coordinates. These 3 coordinates are x-coordinate, y-coordinate and z-coordinate. In three-dimensional space, there is a requirement of three parameters for the purpose of finding the exact location of a point.
Given are two points in 3-dimension, (2,4,12) and (7,4,0), we need to find the distance between them, and the midpoint of the segment for which these are the endpoints,
Distance between two points in 3d is given by =
D = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]
Here, [tex](x_1, y_1, z_1)[/tex] = (2,4,12)
[tex](x_2, y_2, z_2)[/tex] = (7,4,0)
Therefore,
D = [tex]\sqrt{(7-2)^2+(4-4)^2+(0-12)^2}[/tex]
D = [tex]\sqrt{5^2+(-12)^2}[/tex]
D = [tex]\sqrt{25+144}[/tex]
D = [tex]\sqrt{169}[/tex]
D = 13
Therefore, the distance between the given points is 13 units.
Since, the midpoint divide the segment in 1:1 ratio,
Therefore,
(x, y, z) = [tex](\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2},\frac{z_2+z_1}{2} )[/tex]
(x, y, z) = [tex](\frac{7+2}{2}, \frac{4+4}{2},\frac{0+12}{2} )[/tex]
(x, y, z) = (9/2, 8/2, 12/2)
(x, y, z) = (4.5, 4, 6)
Hence, the distance between the given points is 13 units and the coordinates of the midpoint of the segment is (4.5, 4, 6)
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