Question

1. graph the image of the triangle below using a scale factor of k = 3/4. 11. a(-10, -8) is the image of a after a dilation centered at the origin with a scale factor of 2. what are the coordinates of a? 12. p(-2, 5) is the image of p after a dilation centered at the origin with a scale factor of 1/3. what are the coordinates of p? 13. z(3, 8) is the image of z after a dilation centered at the origin with a scale factor of 3/2. what are the coordinates of z? 14. h(1.5, -4) is the image of h after a dilation centered at the origin with a scale factor of 1/2. what are the coordinates of h?

Explanation:

Step1: Fórmula de dilatación

Si \(A'(x', y')\) es la imagen de \(A(x,y)\) después de una dilatación centrada en el origen con factor de escala \(k\), entonces \(x' = kx\) y \(y'=ky\). Entonces \(x=\frac{x'}{k}\) y \(y = \frac{y'}{k}\).

Step2: Aplicar la fórmula para \(A'\)

Dado \(A'(- 10,-8)\) y \(k = 2\).
Para la coordenada \(x\) de \(A\): \(x=\frac{-10}{2}=-5\).
Para la coordenada \(y\) de \(A\): \(y=\frac{-8}{2}=-4\).

Answer:

Las coordenadas de \(A\) son \((-5,-4)\)