Question Video: Determining the Plane in Which a Given Point Lies Mathematics • Third Year of Secondary School

Video Transcript

In which of the following coordinate planes does the point negative seven, negative eight, zero lie? Is it (A) the 𝑥𝑦-plane, (B) the 𝑥𝑧-plane, or (C) the 𝑦𝑧-plane?

We know that any point in three dimensions has an 𝑥-, 𝑦-, and 𝑧-coordinate. In this question, the 𝑥-coordinate is negative seven, the 𝑦-coordinate is negative eight, and the 𝑧-coordinate is zero. As 𝑧 is equal to zero, the point will not move in the direction of the 𝑧-axis. We can therefore conclude that as 𝑧 is equal to zero, the point will lie on the 𝑥𝑦-plane. If our 𝑦-coordinate was equal to zero but 𝑥 and 𝑧 had a positive or negative value, the point would lie in the 𝑥𝑧-plane. In a similar way, a point would lie in the 𝑦𝑧-plane if it had coordinate zero, 𝑦, 𝑧, where 𝑦 and 𝑧 are positive or negative values.