Question

finding the vertex from the pre-image
the rule for the dilation of quadrilateral qrst to the image qrst is ( d_{o,0.5}(x, y) \to (0.5x, 0.5y) ). what are the coordinates of q, if q(0, 2)?
(\boxed{ }, \boxed{ })
grid image of quadrilateral qrst with q at (0,2), r, s, t on grid

Explanation:

Step1: Identify the dilation rule

The dilation rule is \( D_{O,0.5}(x, y) \to (0.5x, 0.5y) \), where \( (x, y) \) are the coordinates of the pre - image point.

Step2: Substitute the coordinates of Q into the rule

For point \( Q(0, 2) \), we substitute \( x = 0 \) and \( y = 2 \) into the dilation rule \( (0.5x, 0.5y) \).
First, calculate the \( x \) - coordinate of \( Q' \): \( 0.5\times x=0.5\times0 = 0 \)
Then, calculate the \( y \) - coordinate of \( Q' \): \( 0.5\times y = 0.5\times2=1 \)

Answer:

\( (0, 1) \)