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STEP Support Programme

Step Foundations Assignment 5

Question 2(ii) I am not familiar with coordinates with three-values. Is it referring to an xyz-plane? I don't understand how to find the fourth vertex and how to find the base area. Could someone please explain?

You are correct in assuming that the coordinates are referring to a point in the $xyz$ plane - the first coordinate is the displacement in the $x$ direction, the second is the displacement in the $y$ direction and the third is the displacement in the $z$ direction. Here is a bit of an explanation about how they work.

The rectangular base of the pyramid is is the $xy$ plane, so the $z$ coordinate will be $0$. One of the vertices is a displacement of 4 unit in the $x$ direction from the origin - $(0,0,0)$ and another is a displacement of 6 units in the $y$ direction from the origin. To get to the last vertex of the rectangle you need to go 4 units in the $x$ direction and 6 units in the $y$ direction, so it will be at $(4, 6, 0)$.