Question

finding the vertex from the pre - image
the rule for the dilation of quadrilateral qrst to the image qrst is ( d_{0,0.5}(x,y)\to(0.5x,0.5y) ). what are the coordinates of q, if ( q(0,2) )?

Explanation:

Step1: Apply the dilation rule to the x - coordinate

Given the dilation rule \(D_{(0,0.5)}(x,y)\to(0.5x,0.5y)\) and the point \(Q(0,2)\). For the x - coordinate of \(Q\), \(x = 0\). Using the rule \(x'=0.5x\), we substitute \(x = 0\) into it: \(x'=0.5\times0\).

$$x' = 0$$

Step2: Apply the dilation rule to the y - coordinate

For the y - coordinate of \(Q\), \(y = 2\). Using the rule \(y'=0.5y\), we substitute \(y = 2\) into it: \(y'=0.5\times2\).

$$y'=1$$

Answer:

\((0,1)\)