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23 hours ago · Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...
3 days ago · Coordinate Graphs. Coordinate graphs, or coordinate planes, are grids with two main axes (lines) labeled x and y. The points where any two lines intersect are labeled based on their distance from these two axes. For instance, two lines that intersect at (3, 5) would be three points above the x-axis and five points to the right of the y-axis.
2 days ago · Scatter plots show how two continuous variables are related by putting one variable on the x-axis and a second variable on the y-axis. A scatter plot for regression includes the response variable on the y-axis and the input variable on the x-axis.
1 day ago · By definition of a function, the image of an element x of the domain is always a single element of the codomain. However, the preimage f − 1 ( y ) {\displaystyle f^{-1}(y)} of an element y of the codomain may be empty or contain any number of elements.
2 days ago · A basic 3D rotation (also called elemental rotation) is a rotation about one of the axes of a coordinate system. The following three basic rotation matrices rotate vectors by an angle θ about the x-, y-, or z-axis, in three dimensions, using the right-hand rule—which codifies their alternating signs.
2 days ago · Definition: Dilation in the Vertical Direction. Consider a function 𝑦 = 𝑓 (𝑥), plotted in the 𝑥 𝑦-plane. We stretch it in the vertical direction by a scale factor of 𝑎, causing the transformation 𝑓 (𝑥) → 𝑎 𝑓 (𝑥).
Definition: Intercept Equation of a Plane. The intercept equation of a plane with 𝑥 -, 𝑦 -, and 𝑧 -intercepts 𝑎, 𝑏, and 𝑐, respectively, is given by 𝑥 𝑎 + 𝑦 𝑏 + 𝑧 𝑐 = 1. Let us look at the equation of planes that are parallel to one axis.
