Question

30 quadrilateral efgh is dilated to create quadrilateral efgh using the origin as the center of dilation. which one of the following statements is true? a quadrilateral efgh is dilated by a scale factor of 1/2 to create quadrilateral efgh. b quadrilateral efgh is dilated by a scale factor of 1/3 to create quadrilateral efgh. c quadrilateral efgh is dilated by a scale factor of 2 to create quadrilateral efgh. d quadrilateral efgh is dilated by a scale factor of 3 to create quadrilateral efgh.

Explanation:

Step1: Recall dilation property

Dilation with center at origin multiplies coordinates of each point by scale - factor. If a point $(x,y)$ is dilated with a scale - factor $k$ centered at the origin, the new point is $(kx,ky)$.

Step2: Analyze side - length ratio

Count the lengths of corresponding sides of the original and dilated quadrilaterals. For example, if we consider a side of the original quadrilateral $EFGH$ and its corresponding side in $E'F'G'H'$. If the length of a side of $EFGH$ is $l_1$ and the length of the corresponding side of $E'F'G'H'$ is $l_2$, the scale - factor $k=\frac{l_2}{l_1}$. From the graph, we can see that the sides of $E'F'G'H'$ are half the length of the sides of $EFGH$. So the scale - factor is $\frac{1}{2}$.

Answer:

B. Quadrilateral $EFGH$ is dilated by a scale factor of $\frac{1}{2}$ to create quadrilateral $E'F'G'H'$