Question

Triangle ABC is formed by the vertices A(1,2,-1), B(-3,-6,2)and C(3,-2,0).

Answer 1

Answer:

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

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]:                    $(\frac{-3+3}{2},\frac{-6-2}{2}, \frac{2+0}{2} )$
2. Add/Subtract:                       $(\frac{0}{2},\frac{-8}{2}, \frac{2}{2} )$
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]:                    $d = \sqrt{(0-1)^2+(-4-2)^2+(1+1)^2}$
2. Subtract/Add:                       $d = \sqrt{(-1)^2+(-6)^2+(2)^2}$
3. Exponents:                           $d = \sqrt{1+36+4}$
4. Add:                                      $d = \sqrt{41}$