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Apply the distance and midpoint formula in 3D

LT 10.4 Apply the distance and midpoint formula in 3D

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A diagonal of a three-dimensional figure connects

two vertices of two different faces. Diagonal d of a rectangular prism is shown in the diagram. By the Pythagorean Theorem, 2 + w2 = x2, and x2 + h2 = d2. Using substitution, 2 + w2 + h2 = d2.

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Example 1 Find the length of the diagonal of a 6 cm by 8 cm by 10 cm rectangular prism 14.14 cm

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Example 2 Find the length of the diagonal of a cube with edge length 5 cm. 8.7 cm

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Space is the set of all points in three dimensions.

Three coordinates are needed to locate a point in space. A three-dimensional coordinate system has 3 perpendicular axes: the x-axis, the y-axis, and the z-axis. An ordered triple (x, y, z) is used to locate a point. To locate the point (3, 2, 4) , start at (0, 0, 0). From there move 3 units forward, 2 units right, and then 4 units up.

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Example 3 Find the midpoint of the segment whose endpoints are (3, -6, 5) and (-2, 1, 10) (.5, -2.5, 7.5)

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Example 4 To the nearest tenth, what is the distance between (1, -4, 7) and (-2, -3, -10)? 17.3

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