Question

quadrilateral j k l m was dilated according to the rule d_{o, \frac{1}{2}}(x, y) \
ightarrow\left(\frac{1}{2} x, \frac{1}{2} y\
ight) to create the image quadrilateral j k l m, 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)

Explanation:

Step1: Find the coordinates of \(J'\)

From the graph, the coordinates of \(J'\) are \((0,-2)\)

Step2: Use the dilation rule to find the pre - image

The dilation rule is \(D_{O,\frac{1}{2}}(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)\). Let the coordinates of \(J\) be \((x,y)\). Then \(\frac{1}{2}x = 0\) and \(\frac{1}{2}y=-2\)
Solve for \(x\): \(x = 0\times2=0\)
Solve for \(y\): \(y=-2\times2=-4\)

Answer:

\((0, - 4)\)