Question

Find equations of the line that is parallel to the z-axis and passes through the midpoint between the two points (0, −4, 9) and (−8, 5, 1). (Enter your answers as a comma-separated list of equations.) x=−8, y=5+9t, z=1−8t

Answer 1

Answer: x = -4, y = 0.5, z = 5 +t

Hi!

The line L whose direction is parallel to vector V a passes through point A

is parametrized

$P_L = Vt + A$

Where t, is a real number, and $P_L$ is a any point on line L.

In this case the direction is that of the z-axis , so V = (0, 0, 1)

A is the midpoint between points B = (0, -4, 9) and C=(-8, 5, 1)

The midpoint is A = (B + C)/2 = (-4, 0.5, 5)

Then the line is:

$P_L = (0,0,1) t + (-4, 0.5, 5)$

The equations for each coordinate are:

$x = -4\\y = 0.5\\z = 5 + t$