Question Video: Understanding Standard Position Mathematics

Video Transcript

Does the ordered pair given by the ray joining 𝐶𝐴 and the ray joining 𝐶 to 𝐷 express an angle in standard position?

We know that for an angle to be in standard position, its vertex must be centered at the origin and the initial side must lie on the positive 𝑥-axis. Now, our angle is defined by this ordered pair. So we have the ray joining 𝐶 and 𝐴 and the ray joining 𝐶 and 𝐷. The ray joining 𝐶 to 𝐴 is this one, and that does indeed lie on the positive 𝑥-axis. We know it’s the initial side of our angle because it’s mentioned first. Then the ray that joins 𝐶 to 𝐷 is this one here, meaning the angle we’re interested in is this one. But does the vertex of this lie at the origin? Well, no, the vertex is over here somewhere. It’s someway along the positive 𝑥-axis. And so the ordered pair defined by the ray joining 𝐶 to 𝐴 and the ray joining 𝐶 to 𝐷 does not express an angle in standard position. And the answer is no.

There are, however, a couple of angles that are in standard position here. The first would be given by the ordered pair the ray joining 𝑂 to 𝐶 and the ray joining 𝑂 to 𝐸. The ray 𝑂𝐶 lies on the positive 𝑥-axis, and then the vertex is centered at the origin. Similarly, we could begin with the same initial side, and that’s the ray joining 𝑂 to 𝐶, and measure through to the ray joining 𝑂 to 𝐺. The vertex for this angle is still located at the origin, and so the angle is also in standard position.