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: Substitute the coordinates of \(Q\) into the dilation rule

Given the dilation rule \(D_{0,0.5}(x,y)\to(0.5x,0.5y)\) and \(Q(0,2)\), substitute \(x = 0\) and \(y=2\) into the formula.
For the \(x\) - coordinate: \(0.5\times x=0.5\times0\)
For the \(y\) - coordinate: \(0.5\times y = 0.5\times2\)

Step2: Calculate the new coordinates

For the \(x\) - coordinate: \(0.5\times0 = 0\)
For the \(y\) - coordinate: \(0.5\times2=1\)

So the coordinates of \(Q'\) are \((0,1)\)

Answer:

$(0,1)$