A Moving Point

I have constructed a red point 𝐴 + 𝑇(𝐸 - 𝐴) that travels from A to E. I gave it the name P because I want to easily refer to it again. I used T {0 ≤ T ≤ 1} for the parameter that moves the point and as soon as I typed it, Desmos asked me to make a slider. At the moment captured in the screen-shot above, the point has completed 60% of its journey from A to E.

Note carefully the relationship between the two similar formulae: 𝐴 + 𝑡(𝐸 − 𝐴) and 𝐴 + 𝑇(𝐸 − 𝐴)

The first draws a line, the second moves point. One way to say this is that t delivers changes in space and T gives us changes in time.

Now you try: Animate a point moving along the line you graphed in the last activity.