quadrilateral jklm was dilated according to the rule $d_{o,\frac{1}{2}}(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$…

quadrilateral jklm was dilated according to the rule $d_{o,\frac{1}{2}}(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$ to create the image quadrilateral jklm, which is shown on the graph. what are the coordinates of vertex j of the pre - image? (0, - 4) (0, - 1) (0, 0) (0, 4)

quadrilateral jklm was dilated according to the rule $d_{o,\frac{1}{2}}(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$ to create the image quadrilateral jklm, which is shown on the graph. what are the coordinates of vertex j of the pre - image? (0, - 4) (0, - 1) (0, 0) (0, 4)

Answer

Explanation:

Step1: Recall dilation rule

The dilation rule is $D_{O,\frac{1}{2}}(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$. To find the pre - image from the image, we use the reverse operation. If $(x',y')$ is the image and $(x,y)$ is the pre - image, then $x = 2x'$ and $y = 2y'$.

Step2: Identify coordinates of J'

From the graph, the coordinates of vertex $J'$ of the image are $(0, - 2)$.

Step3: Calculate coordinates of J

Let $(x',y')=(0,-2)$. Then $x = 2x'=2\times0 = 0$ and $y = 2y'=2\times(-2)=-4$.

Answer:

(0, - 4)