Question

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

Answer 1

Point D:
`(0,-4, 1 )`

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]:
  `((x_1+x_2)/(2),(y_1+y_2)/(2), (z_1+z_2)/(2) )`
• Distance Formula [3D]:
  `d = √((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`

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]:
   `((-3+3)/(2),(-6-2)/(2), (2+0)/(2) )`
2. Add/Subtract:
   `((0)/(2),(-8)/(2), (2)/(2) )`
3. Divide:
   `(0,-4, 1 )`

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]:
   `d = √((0-1)^2+(-4-2)^2+(1+1)^2)`
2. Subtract/Add:
   `d = √((-1)^2+(-6)^2+(2)^2)`
3. Exponents:
   `d = √(1+36+4)`
4. Add:
   `d = √(41)`