Question

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: Substitute the coordinates into the dilation rule

Given the dilation rule \(D_{O,0.5}(x,y)\to(0.5x,0.5y)\) and the point \(Q(0,2)\). Here \(x = 0\) and \(y=2\).

Step2: Calculate the new \(x\) - coordinate

For the \(x\) - coordinate of \(Q'\), use the formula \(x'=0.5x\). Substitute \(x = 0\) into it: \(x'=0.5\times0 = 0\).

Step3: Calculate the new \(y\) - coordinate

For the \(y\) - coordinate of \(Q'\), use the formula \(y'=0.5y\). Substitute \(y = 2\) into it: \(y'=0.5\times2=1\).

Answer:

$(0,1)$