Question

In space the magnitude of a line segment whose starting point (1,0,9) and ending point (-4,10,4) is

Answer 1

To find the magnitude of a line segment in space, we use the distance formula. Using the given points (1,0,9) and (-4,10,4), we can calculate the magnitude to be approximately 12.25.

Step-by-step explanation:

To find the magnitude of a line segment in space, we use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Using the given points (1,0,9) and (-4,10,4), we can plug in the values into the distance formula:

d = sqrt((-4 - 1)^2 + (10 - 0)^2 + (4 - 9)^2)

Simplifying the equation, we get:

d = sqrt((-5)^2 + 10^2 + (-5)^2)

d = sqrt(25 + 100 + 25)

d = sqrt(150)

Therefore, the magnitude of the line segment is sqrt(150), which is approximately 12.25.