User:
• Matrices
• Algebra
• Geometry
• Funciones
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Ecuación de una recta Equation of a line (from graph) Quadratic function Posición relativa de dos rectas Asymptotes Limits Distancias Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product

Dilations: find the coordinates

In a coordinate plane, dilations whose center are the origin have the property that the image of P(x,y) is P'(kx,ky) where k is the scale factor of the dilation.

Draw a dilation of rectangle ABCD with A(2,2), B(6,2), C(6,4), and D(2,4). Use the origin as the center and use a scale factor of $\frac{1}{2}$.

Because the center of the dilation is the origin, you can find the image of each vertex by multiplying its coordinates by the scale factor.

 A(2,2) $\rightarrow$ A'(1,1) B(6,2) $\rightarrow$ B'(3,1) C(6,4) $\rightarrow$ C'(6,2) D(2,4) $\rightarrow$ D'(1,2)

Graphycally:

Write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.

S(-5,-5) $\Rightarrow$ S*(,)
T(-5,4) $\Rightarrow$ T*(,)
U(-1,4) $\Rightarrow$ U*(,)
V(-1,-3) $\Rightarrow$ V*(,)