Question

Find the coordinates of the midpoint of the line segment joining the two points. $$ (4,0,-6),(8,8,20) $$

Short answer

The coordinates of the midpoint of the line segment joining the two points (4,0,-6) and (8,8,20) are (6,4,7)

Step-by-step solution

Identify the coordinates of the two points

The two points are (4,0,-6) and (8,8,20). So, \(x_1 = 4\), \(y_1 = 0\), \(z_1 = -6\), \(x_2 = 8\), \(y_2 = 8\) and \(z_2 = 20\)

Apply the midpoint formula

Using the midpoint formula, the coordinates of the midpoint would be \(\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}, \frac{z_1+z_2}{2} \right)\). Substituting the values into the formula gives: \(\left( \frac{4 + 8}{2}, \frac{0 + 8}{2}, \frac{-6 + 20}{2} \right)\)

Compute the results

So, the midpoint coordinates are \(\left( \frac{12}{2}, \frac{8}{2}, \frac{14}{2} \right) = (6,4,7)\)