Question

26 quadrilateral efgh is dilated using the origin as the center of dilation to create quadrilateral efgh. what rule best represents the dilation applied to quadrilateral efgh to create quadrilateral efgh? a (x, y)→(4x, 4y) b (x, y)→(3x, 3y) c (x, y)→(4x, 3y) d (x, y)→(3x, 4y)

Explanation:

Step1: Recall dilation rule

For a dilation with center at the origin $(0,0)$ and scale - factor $k$, the rule is $(x,y)\to(kx,ky)$.

Step2: Find a point and its image

Let's take a point on quadrilateral $EFGH$, say $E(2,4)$. Its image $E'(8,16)$ on $E'F'G'H'$.

Step3: Calculate the scale - factor

To find the scale - factor $k$ for the $x$ - coordinate: $\frac{x_{E'}}{x_E}=\frac{8}{2} = 4$. To find the scale - factor $k$ for the $y$ - coordinate: $\frac{y_{E'}}{y_E}=\frac{16}{4}=4$.

Answer:

A. $(x,y)\to(4x,4y)$