Engineers use three-dimensional coordinates to design construction projects. An overhead light is anchored at point (7, 12, 10) in a design where the floor of the building is represented by the two-dimensional coordinate plane (x-axis and y-axis). Measurements are in feet.

1. Lights are spaced from the hanging light, 4 feet away in the x-direction and 4 feet in the y-direction. Select the possible coordinates of the anchors for two other lights.

a. (3, 8, 10) and (11, 16, 10)
b. (3, 8, 6) and (11, 16, 14)
c. (3, 12, 10) and (11, 12, 10)
d. (7, 8, 10) and (7, 16, 10)

Question

Engineers use three-dimensional coordinates to design construction projects. An overhead light is anchored at point (7, 12, 10) in a design where the floor of the building is represented by the two-dimensional coordinate plane (x-axis and y-axis). Measurements are in feet. 

1. Lights are spaced from the hanging light, 4 feet away in the x-direction and 4 feet in the y-direction. Select the possible coordinates of the anchors for two other lights.

a. (3, 8, 10) and (11, 16, 10)
b. (3, 8, 6) and (11, 16, 14)
c. (3, 12, 10) and (11, 12, 10)
d. (7, 8, 10) and (7, 16, 10)

anonymous · Answer

I think, in the answer, 10 should be the number for z in (x,y,z), because the height of the ceiling remains constant. so I think what you're looking for, is two other lights that are 4 feet away in x and y, but still at 10 for z

anonymous · Answer

so like x has to be four away from y???

anonymous · Answer

no. think of x and y as independent. the directions say we want lights that are 4 feet away in x, and 4 feet away in y, but constant at 10 in z. so if we have one light at the point (7,12,10), where can we put more lights?

anonymous · Answer

ooooh, so itll be 11, 16. 10?

anonymous · Answer

that's one of them. we can also go the other way and say we want a light at (3,8,10) since that meets our requirements too

anonymous · Answer

oh, okay! thanks! i have another question think you might be able to help?

anonymous · Answer

sure

anonymous · Answer

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anonymous · Answer

The roof lines of a building can be described by the system of equations below, where the floor is represented by the x-axis and the y-axis and the height of the building is along the z-axis. Measurements are in feet.

anonymous · Answer

what do you need to do with this?

anonymous · Answer

i have to find xyz, i suck at algebra 2 :c sorry lol

anonymous · Answer

that's okay. there's one thing we can try called gaussian elimination. are you familiar?

anonymous · Answer

nope...

anonymous · Answer

I'm working on the problem. were you taught how to do a problem like this using substitution?

anonymous · Answer

i go to online school so it's kinda like they just give you a problem and you have to solve it on your own....

anonymous · Answer

alright. give me a sec. I can show you how to do it one way

anonymous · Answer

alright

anonymous · Answer

I think you should probably put this into another question for other people to help you with - I can't remmeber quite how to do this the algebra 2 way

anonymous · Answer

alright