Amedian of a triangle is a line segment joining a vertex to the midpoint of the opposite side. find the lengths of the median of the triangle with vertices a(1,2,3), b(-2,0,5), and c(4,1,5)

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Step-by-step explanation:

The given points are A(1,2,3), B(-2,0,5) and C(4,1,5). The triangle is represented in the attach file where the three possible median are length AE, BF, and CD. We determine the coordinate of point D,E and F using the midpoint equation which is for any point A(x,y,z) and point B(a,b,c), the midpoint D is determine by

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Hence going by the above formula we determine the coordinate of point D,E and F

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point E

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Point F

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To determine the length of each median line we use the formula for distance between two points which is express as

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Using the above formula we determine the length of line AE,BF and CD.

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For point BF

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For point CD

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the answer is 62.8 cubic units

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.