Question

Find the distance from (3, −4, 8) to each of the following. (a) the xy-plane √7 (b) the yz-plane (0,−4,8) (c) the xz-plane (3,0,8) (d) the x-axis (3,0,0) (e) the y-axis (0,−4,0) (f) the z-axis (0,0,8)

Answer 1

a) 8 units

b) 3 units

c) 4 units

d)
`4√(5)\text{ units}`

e)
`√(73)\text{ units}`

f) 5 units

Explanation:

We are given the following:

Point (3, −4, 8)

We have to find the distance of the point from the following:

Distance formula:

`(x_1,y_1,z_1),(x_2,y_2,z_2)\\\\d = √((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2)`

(a) the xy-plane

We have to find the distance from (3, −4, 8) to (3, −4, 0)

`d = √((3-3)^2 + (-4+4)^2 + (0-8)^2) = 8\text{ units}`

(b) the yz-plane

We have to find the distance from (3, −4, 8) to (0, −4, 8)

`d = √((0-3)^2 + (-4+4)^2 + (8-8)^2) = 3\text{ units}`

(c) the xz-plane

We have to find the distance from (3, −4, 8) to (3, 0, 8)

`d = √((3-3)^2 + (0+4)^2 + (8-8)^2) = 4\text{ units}`

(d) the x-axis

We have to find the distance from (3, −4, 8) to (3, 0, 0)

`d = √((3-3)^2 + (0+4)^2 + (0-8)^2) = √(80) = 4√(5)\text{ units}`

(e) the y-axis (0,−4,0)

We have to find the distance from (3, −4, 8) to (0, -4, 0)

`d = √((0-3)^2 + (-4+4)^2 + (0-8)^2) = √(73)\text{ units}`

(f) the z-axis (0,0,8)

We have to find the distance from (3, −4, 8) to (0, 0, 8)

`d = √((0-3)^2 + (0+4)^2 + (8-8)^2) = √(25) = 5\text{ units}`