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Triangle ABC is formed by the vertices A(1,2,-1), B(-3,-6,2)and C(3,-2,0).
If D is the midpoint of BC, the the length (distance) of AD.
write the midpoint
write the distance

Respuesta :

Space

Answer:

Point D: [tex](0,-4, 1 )[/tex]

d = √41

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Pre-Calculus

  • Midpoint Formula [3D]: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}, \frac{z_1+z_2}{2} )[/tex]
  • Distance Formula [3D]: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Point A(1, 2, -1)

Point B(-3, -6, 2)

Point C(3, -2, 0)

Step 2: Find Point D

Simply plug in your coordinates B and C into the midpoint formula to find midpoint

  1. Substitute [MF]:                    [tex](\frac{-3+3}{2},\frac{-6-2}{2}, \frac{2+0}{2} )[/tex]
  2. Add/Subtract:                       [tex](\frac{0}{2},\frac{-8}{2}, \frac{2}{2} )[/tex]
  3. Divide:                                  [tex](0,-4, 1 )[/tex]

Step 3: Find distance d

Simply plug in the 2 coordinates A and D into the distance formula to find distance d

  1. Substitute [DF]:                    [tex]d = \sqrt{(0-1)^2+(-4-2)^2+(1+1)^2}[/tex]
  2. Subtract/Add:                       [tex]d = \sqrt{(-1)^2+(-6)^2+(2)^2}[/tex]
  3. Exponents:                           [tex]d = \sqrt{1+36+4}[/tex]
  4. Add:                                      [tex]d = \sqrt{41}[/tex]

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