Question

use the graph at the right. find the vertices of the image of qrtw for a dilation with center (0,0) and a scale factor of \\(\frac{1}{2}\\)\\(\quad\\)\\(q\square\\)\\(\quad\\)(simplify your answer. type an ordered pair.)

Explanation:

Step1: Identify coordinates of Q

From the graph, the coordinates of point \( Q \) are \( (-2, 4) \).

Step2: Apply dilation formula

For a dilation with center \( (0,0) \) and scale factor \( k=\frac{1}{2} \), the new coordinates \( (x', y') \) of a point \( (x, y) \) are given by \( x' = kx \) and \( y' = ky \).
Substitute \( x = -2 \), \( y = 4 \), and \( k=\frac{1}{2} \) into the formula:
\( x'=\frac{1}{2}\times(-2)= -1 \)
\( y'=\frac{1}{2}\times4 = 2 \)

Answer:

\( (-1, 2) \)