Question

quadrilateral fghj is dilated according to the rule
( d _ { o , \frac { 2 } { 3 } } ( x , y )
ightarrow left( \frac { 2 } { 3 } x , \frac { 2 } { 3 } y
ight) ) to create the image quadrilateral
( f ^ { prime } g ^ { prime } h ^ { prime } j ^ { prime } ), which is not shown.
what are the coordinates of point ( j ^ { prime } )?
( ( - 2 , - 4 ) )
( ( - 2 , - 6 ) )
( left( - \frac { 9 } { 2 } , - 4
ight) )
( left( - \frac { 9 } { 2 } , - 9
ight) )

Explanation:

Step1: Find the coordinates of point J

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

Step2: Apply the dilation rule \(D_{O,\frac{2}{3}}(x,y)\to(\frac{2}{3}x,\frac{2}{3}y)\)

For \(x = - 3\), \(\frac{2}{3}x=\frac{2}{3}\times(-3)=-2\).
For \(y=-6\), \(\frac{2}{3}y=\frac{2}{3}\times(-6)=-4\).

Answer:

\((-2,-4)\)