Question

quadrilateral fghj is dilated according to the rule ( d_{o,\frac{2}{3}}(x,y)\to(\frac{2}{3}x,\frac{2}{3}y) ) to create the image quadrilateral fghj, which is not shown. what are the coordinates of point j? ( (-2,-4) ) ( (-2,-6) ) ( (-\frac{9}{2},-4) ) ( (-\frac{9}{2},-9) )

Explanation:

Step1: Find the coordinates of point J

From the graph, the coordinates of point \( J\) are \((- 3,-6)\)

Step2: Apply the dilation rule

The dilation rule is \(D_{O,\frac{2}{3}}(x,y)\to(\frac{2}{3}x,\frac{2}{3}y)\)
Substitute \(x=-3\) and \(y = - 6\) into the rule:
For the \(x\)-coordinate: \(\frac{2}{3}\times(-3)=-2\)
For the \(y\)-coordinate: \(\frac{2}{3}\times(-6)=-4\)

Answer:

\((-2,-4)\)