# Distance From a Plane To A Point, with projections help (finding distance in 3D)

#### kyle1

##### New member
A construction company has a job to knock down the old mall. They have a crane to help them do this. The mall roof is given by the equation .5x + y + 5z = 1. The crane is located at the point (0, 0, 0).
What is the distance between the roof and the crane?

Basically I have no idea how to start this, my teacher barely mentioned projections, though from googling that is all I can find on how to work out this problem. Anyone who could provide me with a couple of beginning steps would be greatly appreciated.

#### stapel

##### Super Moderator
Staff member
A construction company has a job to knock down the old mall. They have a crane to help them do this. The mall roof is given by the equation .5x + y + 5z = 1. The crane is located at the point (0, 0, 0).
What is the distance between the roof and the crane?

Basically I have no idea how to start this, my teacher barely mentioned projections, though from googling that is all I can find on how to work out this problem. Anyone who could provide me with a couple of beginning steps would be greatly appreciated.
What do you mean by "projections...is...how to work out this problem"? What search terms did you use (other than "distance point plane") that led you to "projections"? Since your instructor "barely mentioned projections" (and apparently your textbook hasn't mentioned them at all), why do you believe that this is the way to proceed? Why are you not supposed to find the distance using a formula meant for finding the distance between a point and a plane (such as here)?

Thank you!