Analytic Geometry in the Plane

 

Consider the Cartesian rectangular coordinate system in the plane. Taking the projection of any point М₁ on the x and y coordinate we obtain two numbers x=a₁ and y=b₁. Take two numbers a₂ and b₂ plot a₂ on the x-axis and b₂ on the y-axis . Having drawn two straight lines parallel to the coordinate axes through these points we find obtain a point M₂ in their intersection.

y

a2

M2(a2;b2)

b2

M1(a1;b1) b1

		x

0

a1

Thus, there is a one–to–one correspondence between points in the plane and pairs of numbers.