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

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

Where t, is a real number, and 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:

The equations for each coordinate are:

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6