### Video Transcript

π΄ and π΅ are two points in an
orthonormal coordinate plane with a positive horizontal π₯-axis pointing to the
right and a positive vertical π¦-axis pointing up. The unit lengths of the axes are
given by the grid. If the coordinates of π΄ are one,
two, what are the coordinates of π΅?

Our points π΄ and π΅ are in an
orthonormal coordinate plane. And thatβs a plane whose unit
lengths are given by the grid. Now remember, an orthonormal
coordinate plane is plane π; πΌ, π½ whose axes ππΌ and ππ½ are perpendicular,
thatβs the π₯- and π¦-axes, and whose unit lengths ππΌ and ππ½ are equal. To find the coordinates of the
point π΅, we must first determine the position of the origin of the coordinate
plane. We can do this using the given
point π΄. We know that π΄ has coordinates
one, two. And this means that π΄ sits one
unit to the right of the origin and two units up from the origin. And so working backwards, the
origin is one unit left from π΄ and two units down from π΄.

So now if we find the position of
π΅ with respect to this origin, we see that the point π΅ is one unit length left
from the origin π, that is, negative one unit, and is on the horizontal or π₯-axis,
which means we have zero units in the π¦-direction. The coordinates of π΅ are therefore
negative one, zero.