Video Transcript
Given that the point 𝑥, 𝑦, 𝑧 lies in the 𝑥𝑦-plane, determine its 𝑧-coordinate.
In this question, we’re given a three-dimensional point 𝑥, 𝑦, 𝑧. And we’re told that this point lies in the 𝑥𝑦-plane. We need to use this information to determine the 𝑧-coordinate of our point. There’s a few different ways of answering this question. One way is to look at this graphically. Let’s start by recalling what it means for a point to be on the 𝑥𝑦-plane graphically. The 𝑥𝑦-plane is the set of all points which we get by taking 𝑧-coordinate equal to zero.
Essentially, we’re just letting the 𝑥-coordinate or the 𝑦-coordinate be whatever they want. However, the 𝑧-coordinate has to be equal to zero. So in particular, if 𝑃 is any point on our 𝑥𝑦-plane, 𝑃 will have the form 𝑎, 𝑏, zero, where 𝑎 and 𝑏 can be any real number. And we can use this to determine the 𝑧-coordinate of the point given to us in the question. We know the 𝑧-coordinate of any point on the 𝑥𝑦-plane is zero. So the 𝑧-coordinate of the point given to us in the question must be equal to zero.
