Identify the distance between points (−3,−6,7) and (−9,5,−4), and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary.

Step-by-step explanation:

LET THE Point 1 A and point 2 is B

(AB) ^2=(-9-(-3))^2+ (5-(-6))^2+(-4-7)^2=278

AB=16.67 length unit

Midpoint

X=-9-3/2 =-6

Y=5-6/2=-0.5

Z=-4+7/2=-1.5

The distance between points (−3,−6,7) and (−9,5,−4) is 16.6 units, and midpoints are (-6, -0.5, -1.5).

Distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is determined by the following as D² = (x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²

The midpoint of the line joining  (x₁, y₁, z₁) and (x₂, y₂, z₂)  is given by :

{(x₂+x₁)/2 , (y₂+y₁)/2 , (z₂+z₁)/2}

To determine the distance between points (−3,−6,7) and (−9,5,−4)

Let mid points X, Y, and Z

The given points :  (−3,−6,7) and (−9,5,−4)

Distance between points  (−3,−6,7) and (−9,5,−4) :

D² = (x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²

D² =(-9-(-3))²+ (5-(-6))²+(-4-7)² = 278

D = √278

D = 16.6 units

The midpoint of the line joining (−3,−6,7) and (−9,5,−4) :

X = (-9-3)/2 = -6

Y =(5-6)/2 = -0.5

Z =(-4+7)/2 = -1.5

Hence, the distance between points (−3,−6,7) and (−9,5,−4) is 16.6 units, and midpoints are (-6, -0.5, -1.5).

Learn more about the distance between two points here:

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