Answer:
a) 8 units
b) 3 units
c) 4 units
d) ![4\sqrt{5}\text{ units}](https://tex.z-dn.net/?f=4%5Csqrt%7B5%7D%5Ctext%7B%20units%7D)
e) ![\sqrt{73}\text{ units}](https://tex.z-dn.net/?f=%5Csqrt%7B73%7D%5Ctext%7B%20units%7D)
f) 5 units
Step-by-step 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 = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}](https://tex.z-dn.net/?f=%28x_1%2Cy_1%2Cz_1%29%2C%28x_2%2Cy_2%2Cz_2%29%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%20%2B%20%28y_2-y_1%29%5E2%20%2B%20%28z_2-z_1%29%5E2%7D)
(a) the xy-plane
We have to find the distance from (3, −4, 8) to (3, −4, 0)
![d = \sqrt{(3-3)^2 + (-4+4)^2 + (0-8)^2} = 8\text{ units}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%283-3%29%5E2%20%2B%20%28-4%2B4%29%5E2%20%2B%20%280-8%29%5E2%7D%20%3D%208%5Ctext%7B%20units%7D)
(b) the yz-plane
We have to find the distance from (3, −4, 8) to (0, −4, 8)
![d = \sqrt{(0-3)^2 + (-4+4)^2 + (8-8)^2} = 3\text{ units}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%280-3%29%5E2%20%2B%20%28-4%2B4%29%5E2%20%2B%20%288-8%29%5E2%7D%20%3D%203%5Ctext%7B%20units%7D)
(c) the xz-plane
We have to find the distance from (3, −4, 8) to (3, 0, 8)
![d = \sqrt{(3-3)^2 + (0+4)^2 + (8-8)^2} = 4\text{ units}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%283-3%29%5E2%20%2B%20%280%2B4%29%5E2%20%2B%20%288-8%29%5E2%7D%20%3D%204%5Ctext%7B%20units%7D)
(d) the x-axis
We have to find the distance from (3, −4, 8) to (3, 0, 0)
![d = \sqrt{(3-3)^2 + (0+4)^2 + (0-8)^2} = \sqrt{80} = 4\sqrt{5}\text{ units}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%283-3%29%5E2%20%2B%20%280%2B4%29%5E2%20%2B%20%280-8%29%5E2%7D%20%3D%20%5Csqrt%7B80%7D%20%3D%204%5Csqrt%7B5%7D%5Ctext%7B%20units%7D)
(e) the y-axis (0,−4,0)
We have to find the distance from (3, −4, 8) to (0, -4, 0)
![d = \sqrt{(0-3)^2 + (-4+4)^2 + (0-8)^2} = \sqrt{73}\text{ units}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%280-3%29%5E2%20%2B%20%28-4%2B4%29%5E2%20%2B%20%280-8%29%5E2%7D%20%3D%20%5Csqrt%7B73%7D%5Ctext%7B%20units%7D)
(f) the z-axis (0,0,8)
We have to find the distance from (3, −4, 8) to (0, 0, 8)
![d = \sqrt{(0-3)^2 + (0+4)^2 + (8-8)^2} = \sqrt{25} = 5\text{ units}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%280-3%29%5E2%20%2B%20%280%2B4%29%5E2%20%2B%20%288-8%29%5E2%7D%20%3D%20%5Csqrt%7B25%7D%20%3D%205%5Ctext%7B%20units%7D)