Transformation matrices: write the vertex matrix

Learning Objectives Define a vertex matrix and state its purpose in geometric transformations. Identify the vertices of a polygon from a list of coordinates or a graph. Construct a 2xn vertex matrix for a polygon with 'n' vertices. Correctly format a vertex matrix with all x-coordinates in the first row and all corresponding y-coordinates in the second row. Explain the relationship between the number of vertices in a polygon and the number of columns in its vertex matrix. Convert a given vertex matrix back into a set of ordered pair coordinates. Ever wonder how video game characters and digital animations are moved, resized, and rotated on screen? 🎮 It all begins by representing their shape as a special grid of numbers called a vertex matrix! In this tutorial, yo...

TermDefinitionExample VertexA point where two or more lines, curves, or edges meet. In a polygon, a vertex is a corner.For a triangle with corners at points A, B, and C, the vertices are A, B, and C. PolygonA two-dimensional, closed shape made of straight line segments.A square, a triangle, a pentagon, and an octagon are all polygons. Coordinate PairA set of two numbers, (x, y), that specify the location of a point on a Cartesian plane.The point P is located at (4, -3), where 4 is the x-coordinate and -3 is the y-coordinate. MatrixA rectangular array of numbers, symbols, or expressions, arranged in rows and columns.A = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{bmatrix} is a 2x3 matrix (2 rows, 3 columns). Vertex MatrixA matrix that represents the vertices of a polygon. By...

Vertex Matrix Formation For a polygon with vertices $P_1(x_1, y_1), P_2(x_2, y_2), \dots, P_n(x_n, y_n)$, the vertex matrix $V$ is: $V = \begin{bmatrix} x_1 & x_2 & \dots & x_n \\ y_1 & y_2 & \dots & y_n \end{bmatrix}$ This is the standard structure for a vertex matrix. The first row consists of all the x-coordinates of the vertices, and the second row consists of the corresponding y-coordinates. Each column represents one vertex of the polygon. Vertex Matrix Dimensions For a polygon with $n$ vertices, its vertex matrix will always have dimensions $2 \times n$. This rule provides a quick check for correctness. The number of columns in the vertex matrix must always be equal to the number of vertices of the shape. For 2D geometry, the number of rows is...