Question Video: Using a Grid to Determine the Coordinates of a Point in an Orthonormal Coordinate Plane | Nagwa Question Video: Using a Grid to Determine the Coordinates of a Point in an Orthonormal Coordinate Plane | Nagwa

# Question Video: Using a Grid to Determine the Coordinates of a Point in an Orthonormal Coordinate Plane Mathematics

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 (1, 2), what are the coordinates of π΅?

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### 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 thatβs a plane whose unit lengths are given by the grid. Now remember, an orthonormal coordinate plane is plane π; πΌ, π½ whose axes ππΌ and ππ½ are perpendicular, thatβs the π₯- and π¦-axes, and whose unit lengths ππΌ and ππ½ 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.

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