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Find mid point of (4, 3, 6) and (6, 5, 12).
Question

Find mid point of (4, 3, 6) and (6, 5, 12).

A.

(4, 4, 9)

B.

(5, 4, 9)

C.

(5, 4, 3)

D.

(5, 3, 9)

Correct option is B

Formula:Midpoint=(x1+x22,y1+y22,z1+z22)Step-by-Step Calculation:1. Identify the coordinates of points A and B:A(x1,y1,z1)=(4,3,6)B(x2,y2,z2)=(6,5,12)2. Apply the midpoint formula:Midpoint=(4+62,3+52,6+122)3. Simplify each component:Midpoint=(102,82,182)=(5,4,9)\begin{aligned}&\text{Formula:} \\&\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \\[10pt]&\textbf{Step-by-Step Calculation:} \\[5pt]&1. \ \text{Identify the coordinates of points } A \text{ and } B: \\&\quad A(x_1, y_1, z_1) = (4, 3, 6) \\&\quad B(x_2, y_2, z_2) = (6, 5, 12) \\[5pt]&2. \ \text{Apply the midpoint formula:} \\&\quad \text{Midpoint} = \left( \frac{4 + 6}{2}, \frac{3 + 5}{2}, \frac{6 + 12}{2} \right) \\[5pt]&3. \ \text{Simplify each component:} \\&\quad \text{Midpoint} = \left( \frac{10}{2}, \frac{8}{2}, \frac{18}{2} \right) = (5, 4, 9)\end{aligned}​​

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